I do both American Kenpo and Danzan Ryu Jujitsu. 97% of the time, I wear my hearing aids when I train as I depend upon them to help me understand and communicate. If I don't wear my hearing aids, I have trouble lip-reading (surprising how much even some sound helps when I lipread).
Since the ear-molds are well fitted, I've never had problems with them falling off when I train. When hearing aid tubes (that connects to the mold and the hearing aid) are new, they're very flexible and don't always hold your aid where it should while in vigorous activity. A few days would be needed before the tubes will become more rigid (due to air and natural sweat) and do their part to hold the aids in place. The aid cases are by design, relatively air/water tight, so sweat in general will not bother them, but they're not water-proof though, so be sure to allow your aids to air-dry afterwards. You can choose to have "waterproof" covers for them if you sweat a lot. I don't bother with those covers anyway as I see very little need personally. My hearing aids haven't had problems with getting wet from sweat--maybe long hair may play a role. Do protect them from excessive water (rainstorms, showers/baths, and swimming).
Yes, they're expensive, but they're really not "fragile". The hearing aids are able to withstand a great deal of physical wear. Aids in a simple fall to the ground generally won't damage them. Just be sure to protect them from unnecessary force (run over by a car, chewed by dogs, an angry toddler throwing them against cement, etc.)
I usually wear my hearing aids when I spar. Since head gear is required, I still wear my aids anyway (but be aware that head gear does present a tighter fit on your ear with the aid, so you want to be sure to find the headgear that fits you comfortably). If it is intense sparring or with certain partners who love head shots, I may just leave my aids off. That's up to you to decide whether to wear when sparring--just personal preference--since it will depend a lot on whether your place of training focuses on head shots.
Jujitsu is a different story. I've had my aids accidentally knocked off twice when I rolled with my partner. Most of the time while I train, I wear them. If I know I will be working on intense groundwork, I will take my hearing aids off anyway since I'll be focused upon the ground grappling and won't need my ears (to hear sounds) for that.
Any further questions or requests for advice, let me know. Good luck!
- Ceicei