Magic Trackpad keeps disconnecting, even when wireless keyboard is fine

For years I have been using a wireless keyboard and magic trackpad together in a Henge Clique, with my mid-2009 MacBook Pro currently running El Capitan (10.11.6).

Lately, without any major hardware or set up changes (no new electronics or wifi bases nearby) my trackpad is frequently losing connection. It then does not reconnect on its own, but if I press the power button once it often will then reconnect, but only briefly. I know this isn't a bluetooth issue with my computer because the wireless keyboard has no problems whatsoever. Could it just be a trackpad getting to the end of its useful life? I've had it roughly since 2013. When it does disconnect, it happens suddenly and then the "connection lost" message appears on the screen.

The other thing is that I notice my trackpad batteries are draining much faster recently. I have to charge them more frequently than my keyboard, even when I switch or rotate the rechargeable batteries between the keyboard and trackpad. However, this issues doesn't occur only when the battery power is low. Even after fully charging them this happens all the time.

I've seen a bunch of posts about fixing bluetooth connections, but none seem to apply to my particular situation where it's just one bluetooth device not working properly, with another one right next to it working fine. Any solutions? I can't say whether or not this problem coincided with any OS update.