I've had this same issue since I bought the speaker. If the volume is too high, the power just cuts out. If you turn the speaker back on, don't adjust volume, and continue, it won't even play. The speaker just dies again immediately. If you lower the volume, it will work. Anecdotally, it happens more frequently with songs that have heavy bass so I think it's related to that.
I'm not an engineer but the only thing I can think of is that there is a short somewhere that occurs when power to the bass ramps up. I suspect we've received defective units and this isn't a problem with all SRS XB20's because there's just not enough complaints online.
I've found a few scattered threads online with ppl asking for help. Never an answer or even a reasonable guess.
I'm pretty much at the point where I'm going to gather some of my engineering friends and we'll dismantle this thing in an effort to figure it out. It'll be fun, but I'm pretty disappointed to be honest. This is a good speaker, but it's painful to use with the power issue.