I normally carry everything I need in my jersey pockets, but sometimes a saddle bag is the less stylish but more functional option (unsupported non stop centuries and such). I've had consistent issues in the past with older (and sometimes even newer) bag's Velcro straps coming loose on rough roads. I found this solution that has worked 100% for my friends and I.
When closing the straps, don't simply push them together. Starting at the top, wiggle the straps back and forth / up and down as you work your way down. This engages as many of the hooks and loops as possible and provides a much stronger connection. Using this method I have never had a bag inadvertently come loose. One bag on my MTB I was about to toss in the trash because it wouldn't hold more than a few minutes of riding has been trouble free since I discovered this method. Maybe it's obvious, maybe everybody else has been doing this forever.. but I thought I'd share my little revelation.