10 year old battery
More likely than not is the battery. They are simple watch batteries in the key fobs. If you go to the dealer stealer, you will be looking at around $220 per key and probably charged for the re-programming.
Do a YouTube search on BMW key and a battery replacement video should come up. DO AT YOUR OWN RISK. It looks fairly straight forward. Be cautious to review the re-programming process for all keys in your possession if you choose this route, which also looks fairly straight forward.
My key is slightly acting up on my '06 but not to the point where I will be doing this process yet. But if it continues to deteriorate I'd rather do this than pay $500+ for the dealer stealer to change a $3 battery.
Hope that helps.