I have bought Humpton Bay fan with lights, operated by remote control. I noticed that once in a while it stops working by itself. One day my neighbour knocked on my door and ask me if I have Humpton Bay fan, because every time I turn it on, it turnes on also in his apartment. Is there any way to solve this problem ?

Change the frequency of the fan and remote. See:

Ceiling fan remote controls - help and FAQ- Ceiling Fans N More (http://www.ceiling-fans-n-more.com/ceiling-fan-remote-controls.php)