I've been using the sponges on four MP40s for about two years now and have only had one come off a couple of times. I'm wondering what 'mode' your MP40 is run since they tend to suck onto or stick to the cage when the mp 40 is running constantly above 5-10%. Also, I've noticed they can stretch out a little over time. When new, they seem to fit more snuggly to the cage. Are yours old? If they feel loose, you might try to take up some of the slack by trying to super glue a small seam of it making it a tighter fit. Or you can bu replacement for a relativity cheap price if you think it's just stretched out.
That said - I do agree with others who say they are a pain and get clogged easy. I see this as a plus and minus, the minus is I have to change them 1-2 times a week to keep the performance/flow up. The plus is they act like a filter sock and catch leftover food. My cleaner shrimp and cowfish have learned this is the place to go after the feed mode is over to get a second meal or a midnight snack. Most of the time they have cleaned all the extra food off by the next morning. I've also noticed they keep the cage mostly free from green algae and coralline, making the cleaning quicker and easier.
Regarding BTA protection, I have searched the Internet high and low for an alternative solution to protect my BTAs that is better than the sponges and I have not found it. The 3d printed cover Philt56 posted above might be the best thing I've seen to date if it replaced the original plastic cage of the MP40 or firmly attaches in a way that is easy to remove. I have experience with a couple of rouge anemones which just like to walk-about randomly and will often inflate and float off their rock to ride the current around the tank. (meaning five are happy and one just decided to take a stroll for no apparent reason). Three separate times the sponges have saved these anemones, but they still somehow get their tentacles through the sponge in into the power head if you don't see them right away. I think this takes a good bit of time (overnight) for this to happen so my point is the 3d printed one would likely protect your BTA for a short period, but I would guess it will quickly lose some of its tentacles if you don't cach it quickly. I guess it always a trade-off... I might look into the 3d printed ones for when I go out of town for more than 3-4 days to provide some protection and keep the flow going strong.