Sounds more like a dirty tactic by Microsoft. As suggested elsewhere for other purposes, try spoofing the user-agent header and see if it still keeps logging you out. The UA header shouldn't have any effect whatsoever, but if it "fixes" the problem, it's yet another case of Microsoft being Microsoft.

(Their excuse will be something like "oh, we don't support other browsers because we can't be sure the software will work properly in them", which skips the fact that 1: it lets you log in using a "bad" browser, which it shouldn't do if it's that dangerous and 2: they're a massive multinational corporation. If they can't put a bit of money towards making things work in the small handful of alien browsers, they're doing it wrong. Probably on purpose.)