AirDrop - Computers can't find each other

Hi,

I've read quite a lot on this forum about AirDrop but didn't find answers to my problem.

I have 2 computers : an iMac 27-inch Mid 2011 and a MacBook Pro 15-inch Early 2013 with a Retina Display.

Both are running Mac OSX 10.8.4.

Those 2 computers share the same WI-FI network made of 2 AirPort Express and a TimeMachine.

No LAN connection.

I would like to transfer files from those two computers to each other with AirDrop but that doesn't work.

If I just turned on my two units and open Finder with AirDrop, they usually find each other easily.

I can transfer a file from my MBP to my iMac but not the other way around (when trying to do so, I get a message telling my that the other computer refused my invitation - if my translation is correct since I use a french version of OS X)

BUT ... and that's very upsetting, after a few minutes (usually 2 to 3 minutes maximum), my two computers don't recognize each other without having done anything ... 😮

I've spent quite a lot of time trying to figure out if my sharing options on both machines are set correctly and, at least, what I'm about sure, they are set the same on the two computers.

I could live without AirDrop but I've heard that AirDrop is arriving in IOS soon as well, so I'd better understand this feature...

I'm sure most of you are much more expert than I am and hope someone can help me with this.

Thanks a lot

Jean