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.
If the speaker is under warranty get it replaced.
Taking the speaker apart to replace the battery will compromise or even destroy the acoustic properties of the speakers. Big Blue Live Wireless Bluetooth Speaker