Hi,
can you upload a "normal" sketch (say, Blink)? I don't know Jeelib, but it is possible that it relies on pin assignments that are not good for the Leonardo.
What happens to you is, partially, expected: when the Leonardo starts it shows as a normal communications device. For about 5 seconds it runs the bootloader and waits for incoming uploads. Then it disconnects and redefines itself as more than one device (a comm device plus mouse plus keyboard). The comm-only device seen by Windows on initial startup is no more valid. Normally it is replaced by a new set of devices, but here Jeelib may be causing troubles. If you can upload a sketch you are at least confident that you have at least restored the Leonardo to its normal state, then you can examine Jeelib and look for potential sources of incompatibility.