Personally, I pronounce the past tense of "beat" (to win at a game) as /biːt/, to sound identical to the infinitive. However, I have heard a few people under the age of 30 and from either the west or outer south of Melbourne pronounce it as /bet/. Does this phenomenon happen in other places? In Melbourne it seems to be socio-economic as the west and outer south are the currently developing regions. Is there any documented information about this? Has it happened recently paralleling "to read" /ɹiːd/ "have read" /ɹed/ or is it a long-standing alternate pronunciation?
The pronunciation /bet/ for the past-tense form of beat seems to be fairly old—it goes back at least two centuries. It seems it was associated with Irish English at one point.
Walker's Critical Pronouncing Dictionary (1791) says the following in the entry for the verb "to beat":
The past tense of this verb is by the English uniformly pronounced like the present. Nay, except in solemn language, the present preterit and participle are exactly the same; while the Irish, more agreeably to analogy, as well as utility, pronounce the preterit as the noun bet, a wager: and this pronunciation, though contrary to English usage, is quite conformable to that general tendency observable in the preterits of irregular verbs, which is to shorten the vowel that is long in the present, as eat, ate (often pronounced et); hear, heard; deal, dealt; mean, meant; dream, dreamt; &c.
An article "Some Notes on Pronunciation" in The Irish Monthly, Vol. 23, No. 261 (Mar., 1895), pp. 145-156, which consists of excerpts from a lecture on pronunciation by the English professor George R. Kingdon, contains a criticism of the prevalence of this pronunciation:
The verb to beat has its perfect tense pronounced exactly as the present; it is absolutely wrong to say, "We bet them by three wickets:" you must say, "We beat them."
This word is also pronounced /bet/ in the US South. It's not new. I can't trace its origins, but I've heard it among certain dialects there. It's reminiscent of a similar pronunciation problem in that region -- pen vs. pin. Again, because the vowels are drawled in those dialects, the words can sound identical.