You shouldn't need lithiums to operate the Brownings. Nor dedicated cards. They tell you this to minimize customer frustration and reduce the amount of calls they handle.
If you clean and format the card each time, that is a good standard practice. You can use alkaline just fine in the Strike Force. Lithiums are good for high frequency video use or for dead of winter temps. If you are just running pics, you can get by just fine with value-branded alkalines. I would NOT use ULTRA speed cards in the Strike Force. Use basic Class 4,6, or 10.
If your Strike Force didn't have the latest firmware, then that should be updated. While I have nothing other than personal experience with this situation - I would pay attention to the battery tray. I believe intermittent contact is being made, thus the pics one week and not the next. I had a Strike force where this happens and a new case made the problem stop. I also found that being very firm with the tray going in, helps.