There's a common myth, and it is a false myth, that Li-ion (and LiPo, essentially the same) rechargeable batteries die in about the same time whether or not used. THIS IS NOT TRUE; there are detailed discussions about this, and I also have personal experience of very long life (at least 10 years) of Li-ion batteries used little (GPS used occasionally) or not at all (spares). The one thing that probably is true is that if a battery is left unused, in a discharged state, for long enough for it to self-discharge below a certain critical point, the protection circuitry may prevent it from ever charging again. In this case possibly rejuvenation will work (as the battery isn't otherwise degraded), but I have no experience or knowledge.
The Zeo battery, in particular, can't be left in a safely charged state (without disassembly), as it transmits until it discharges. I have two transmitters, and alternate them every few months to protect against the voltage dropping below the threshold.
Source on this is the Wikipedia Talk page (not the article) on Lithium-ion battery. Search for "batteryuniversity" - there are several sections on the page discussing this, with very useful information.
Just a small point: you can get rechargeable lithium batteries in the coin formats (any xx2032 is the same size as CR 2032; some of the "xx"s are rechargeable). Not particularity useful here, but I have replaced a dead rechargeable of odd size with a 2032-size rechargeable in a holder.