Is there a maximum number of charging cycles for the VP3300 battery? And if the battery reaches the point where there is little to no capacity, will the card reader continue to function properly when connected to external power?

Answer:

The battery charging cycle is over 300 cycles according to the spec. After the 300 cycles, the battery capacity drops gradually but very slow, the curve is non-linear.

And if the reader connects to external power, no matter the battery is full or empty, the reader will use external power for function. Even if the capacity is almost out, the reader won't power off during a transaction as there is a safe level to avoid this situation.