In many places online you can find statements that the Olympic games were banned by the emperor Theodosius I. The date is variable — 385 through to 393, and the claims are always unreferenced to ancient evidence which should make us all wary.
A little earlier this afternoon I was looking for any evidence. And I came across this:
We owe the notion of the ancient Olympics ending in 393 to John [sic] Cedrenus, who was writing in the eleventh century. A somewhat different tradition was known to the author of a note on a work by the satirist Lucian, who said that the games continued ‘from the time of the Hebrew judges until that of Theodosius the Younger.’
This naturally led me to ask where I might find the text of Cedrenus. And … do you know, I found almost nothing? Why is there no translation of Cedrenus?
Another work made much the same statement:
It is generally assumed that the Olympic games continued to be celebrated as late as the fourth or fifth century of the Christian era. Cedrenus appears to date their suppression in the 16th (potius the 15th) of Theodosius the elder AD 393.[z] Joannes Lydus attributes it to Theodosius the younger[a]: … unless he meant the substitution of some other era for that of the reckoning by Olympiads. The Olympic games are certainly recognised as in existence in the reign of Theodosius the Great [b] and by Moses Chorenensis seem to be so even as late as the 20th of Theodosius the younger[c].
z. Mr Clinton Fasti Romani ad AD 393 Ol 193
a. iv. 64. 95. 22.
b. Anecdota Graeca Paris ii. 155. 17.
c. iii. 40. 279.
These references are not very helpful, of course.
There is this:
We are told by an eleventh-century historian, Kedrenos (Historia comparativa [sic] 322B and 348A), of the last Olympiad (293rd), which occurred under Theodosius I in 393 or 394 before his edict against pagan festivals. Kedrenos reports that the Zeus of Phidias was moved to Constantinople, where it was kept in the palace of the patrician Lausos and was eventually lost in a fire. But the source may well be in error. The edict of Theodosius II on November 13, 426, ordered the destruction of all pagan temples. A late source records the burning down of the Temple of Zeus at that time (scholiast to Lucian’s Rhetorical Precepts 6 Jacobitz). Archaeology shows rather that another earthquake brought down the temple and traces of burning are absent. … In A.D. 395, two years after the edict of Theodosius I, the Goths under Alaric invaded as far as the Peloponnese, although Olympia was probably passed by.
Unfortunately the references to Cedrenus only tell us about the statue. Clinton’s Fasti Hellenici gives a better reference:
The series of years commences at the 55th Olympiad and is brought down to the cessation of the Olympiads a period of 956 years. Censorinus names the second year of Olymp. 254 and Eusebius the second year of Olymp. 277, which he makes coincident with the 20th year of Constantine.
The Olympiads ceased in the reign of Theodosius. Cedrenus having mentioned the 15th and 16th years of Theodosius proceeds thus [a] … The 16th year of Theodosius began xiv Kal. Feb. AD 394 in the middle of Olymp. 293. 1. He died xvi Kal. Feb. AD 395 in the middle of Olymp 293. 2. The 293rd Olympiad therefore appears to have been the last.
The Scholiast, however, upon Lucian[b] brings down the Olympiads a little lower … The younger Theodosius began to reign May AD 408, U.C. Varr. 1161 = Olymp. 296. 4. The Alexandrine Chronicle pursues the computation by Olympiads to Ol. 345 c but there is no proof that the Olympic games actually continued to so late a period. The author merely expresses the Olympiads as a notation of time.
[a] Cedren. p.325 C.
[b]Tom. VII p. 515.
So what does Cedrenus  say, in 326D? Almost nothing, and that little has to be given with reference to other events:
In year 15 and 16 of his reign, Theodosius published a law that no woman should receive money to become a deaconess unless older than 60. In the same year died [p.325D] Placilla, wife of Theodosius, … the people of Antioch threw down his statue because of the exactions of the emperor, because of which John Chrysostom, then a priest in Antioch, published marvellous orations under the title Of the statues.
Then the festival of the Olympics ceased, which it was customary to celebrate at the end of every fourth year. [P327A] It was instituted at the time when Manasses was king of Judah, and continued until the reign of Theodosius. …
Likewise Theodosius overturned all the temples of the fictitious ‘gods’, which Constantine the Great ordered <something>. He died at Milan aged 60 from illness, after reigning 16 years, leaving two sons…
So Cedrenus tells us only that in the last year of the reign of Theodosius, i.e. in 394 AD (unless we wish to include the first few weeks of 395), the Olympics ceased. Interestingly he does NOT say that Theodosius ordered it halted, just that “it stopped”. The climate of the times must have been very hostile to its continuance, it must be said.
Interestingly Cedrenus, a little earlier, in 322B, tells us of various items removed from temples and set up at Constantinople, after the defeat of Eugenius by Theodosius in 394.
In the [palace] of Lausus was … the image of Athena of Lindos, of emerald stone, four feet high, the work of Scyllides and Dipoenus the statue-makers, which was originally given by Sesostris, tyrant of Egypt, as a gift to Cleobulus, the tyrant of Lindos. And the Aphrodite of Cnidos, from white stone, nude, hand over the pudenda, the work of Praxiteles of Cnidos. And the Hera of Samos, the work of Lysippus and Bupalos of Chios. … And the ivory Zeus of Phidias, which Pericles dedicated in the Olympic temple.
So it sounds as if the image was removed from Olympia before the games had ceased; but it is in the same year and it would be strange if the events were unrelated. In 348A we read of the fire at Constantinople that happened in the 5th year of the emperor Marcian. Among the places burned is the palace of Lausus.
Let us move on to the Scholion on Lucian. This reads as follows, in full:
Ὀλυμπιάδας] πόλις ἧν ἐν Ἤλιδι Ὀλυμπία καλουμένη ἱερὸν ἔχουσα ἐπιφανέστατον Ὀλυμπίου Διός. ἐν ταύτῃ ἁγὼν ἐπετελεῖτο παγκόσμιος τὰ Ὀλύμπια κατὰ πέντε ἔτη συγκροτούμενος· διὸ καὶ πενταετηρικὸς ἐκαλεῖτο· ὅς καὶ ἀνεγράφετο τοῖς δημοσίοις ἀεὶ εἰς δήλωσιν τῶν ἐνιαυτῶν καὶ ἧν τοῦτο ἀκριβὴς τῶν χρόνων ἐπίγνωσις· τεσσάρων γὰρ ἐτῶν μεταξὺ διαρρεόντων τῷ πέμπτῳ συνετελεῖτο. καὶ διήρκεσεν ἀρξάμενος ἀπὸ τῶν καθ’ Ἑβραίους κριτῶν μέχρι τοῦ μικροῦ Θεοδοσίου· ἐμπρησθέντος γὰρ τοῦ ἐν Ὀλυμπίᾳ ναοῦ ἐξέλιπε καὶ ἡ τῶν Ἠλείων πανήγυρις.
My Greek is very bad, but my guess at the sense is something like this (corrections welcome!):
Olympiads] The town in Elis, Olympia, is called the manifest temple of Olympian Zeus. In this the Olympic contest common to all the world was celebrated (?) every five years: and because of which (summoned?), falling every four years [i.e. five inclusively]. And the time-span being engraved and setup publicly, indicating the year and the exact date …. And it endured in first place down from the judges of the Hebrews until Theodosius the Younger. For a fire having broken out in the temple of Olympia, the assembly of the Elians abandoned it.
It is not clear from this whether ‘it’ is the system of Olympiads was abandoned after the fire in the temple — which thereby wiped out the public record — or the Olympic contests.
Then there is the reference in John the Lydian, but I have not been able to work out where is meant.
It’s not much, is it? None of this is very conclusive. I would theorise, ignorantly, that the statement of Cedrenus is correct; and that the system of Olympiads continued another 50 years, out of habit (and, after all Eusebius the Christian historian himself used it in his chronicle), as the scholiast states. But who knows?