It mostly depend on battery type, and after that current. Batteries usually dislike very high currents, that would make them charge or discharge faster than in 1 hour, because of heating and secondary reactions, and very low currents, that would make them discharge in a year, because of dendrite formation.
Worst type of battery for decade long work are lithium-ion batteries. Their decay is mostly due to time and temperature, rather than cycles used. Exact opposite of your goal. NiCd, NiMH are less energy dense, they also will need additional 3 recharges per year due to self-discharge. All of them lose about half of their maximum capacity in 3 years. Li-ion because of degradation due to temperature. NiCd and NiMH bevause of large self discharge.
LiFePO4 is significantly longer living battery than li-ion. Lead-acid bartery is somewhat similar for your usage. They will lose about half of their capacity in 10 years. They achieve it in a different way. Lead-acid has significant self-discharge, needing an additional recharge every year, but its bulky and degradation takes a long time to affect it all. LiFePO4 is the opposite, very delicate, low self discharge, and degradation is just slower in general. At this timeframe your device will become obsolete.
Lithium titanate, LTO, is probably the best of what we have today for your usage. It is very durable and degrades very slowly. Its hard to put an estimate on this, but i guess you can expect about 25 years till half of it maximum capacity is gone. At this time frame wires will rust away first.
If you need even longer working time, you could check supercapacitors. They have 10 times less energy density, but they will work till their shell is rusted away. About 50 years till half of of them are rusted. They also need 100 recharges per year due to self discharge.
If you want even longer life, check ordinary capacitors and compound filled PCB. Capacity is 100 times less than batteries. Those will work till UV, ozone and moisture will destroy the compound or wires going to the board. At this time frame your smart PCB components are likely to fail first. About 100 years. Will need a few recharges per year due to selfdischarge.
For longer still, will need something exotic, like flywheels and magnetic levitation in a vacuum chamber.