I used to have the same problem but the guitar was an Ibanez Jumbo type bought in 1978.
The string (always the 3rd) got broken when it was 'cold'. So, what I used to do was to play for some time to get the string 'hot' and then to change the tuning to D or to the standard.
The string gauge could be Light or Medium, but the effect was the same.
With my Avalon I haven't had this problem yet (and strings need to be changed long time ago).