Bacteria and yeast are actually pretty tough little critters. My brewing buddy always says once you brew a sour beer you are very likely to do it again and again without meaning too. The reason is that the nasties get into tiny imperfections (e.g. scratches, etc.) and survive even the most thorough sterilization techniques. So what we can assume is that most likely somewhere along you process you have an infection stowing away that is souring your beer. Knowing where the infection comes from would help, but how many batches do you want to ruin before figuring it out?
Seems most likely that the infection you are seeing is happening during bottling but it could happen at multiple steps in the process and there is really only one way to get rid of the problem. Throw out what you can afford to replace (e.g. tubes, stirring implements, spigots, buckets, etc.). Then for those you can't replace easily sterilize the hell out of them and sterilize for a lot longer than you normally would shaking vigorously. Times like these are good opportunities to take a look at your sterile technique and get paranoid like crazy. Clean and sterilize everything very carefully. I mean everything!
P.S. BIAB is awesome!!! Good choice of mashing techniques.