Kobo not accepting a charge - Kobo Arc

Lithium ION batteries are usually rechargeable. The use mode for these batteries is that there are a set number of recharges that equate to the life of the battery. Usually that life is approximately 1,000 charges.
If you use your battery to 50% then recharge, you can do this ~2,000 times. As the life of the battery is used up, the maximum charge lessens which means where you may have had 8 hours of play time when the battery was new, you will only have 6 hours as the battery life is used up.
In order for a Lithium ION battery to recharge there must be at least a small amount of charge left as a "seed" for that recharge. If you drain a L-ION battery down to zero, it may never recharge again or the max charge will be reduced to an insignificant amount of the original full charge. eg instead of 8 hours you may only get 15 minutes, or 5 minutes, or no minutes.
You are much better off recharging when 50% depleted than using it up til your product stops.
L-ION batteries cannot be repaired only replaced. Most cheap products using L-ION batteries cannot have their batteries replaced.