Contrary to what rkaufmann87 says yes there are reasons to connect the Mac mini to the Receiver.
Firstly the AV Receiver would enable surround sound to be sent over the same HDMI cable from the Mac to the AV receiver, the AV Receiver could then output this to 5.1 speakers, and pass through the video to the projector. I have never heard of a projector that supports surround sound.
Secondly, the AV Receiver may well have multiple HDMI inputs (and other connectors) allowing multiple devices to 'share' the projector, e.g. a DVD/Blu-Ray Player, a set-top box, a games console, and of course the Mac, not to mention an Apple TV etc. In general an AV Receiver is likely to have far more connectors than a projector.
So clearly connecting the Mac mini to the AV Receiver rather than directly to the projector is a sensible scenario. Now with regards to resolving the problem. The standard behaviour of the Mac is that if it is not connected to a live display it 'turns off' the video signal and video chip in the Mac. The reasoning being that if there is no display why waste energy and time sending a signal that is not going to be received by anything. Apart from the fact that this means if you are still running software on the Mac mini and access it via Screen Sharing you will typically find the resolution drops to a lower size, it also means any video processing then has to be done by the CPU rather than the GPU and this actually includes the Screen Sharing video itself as well so Screen Sharing is then slower. It also means that audio reverts to going to the built-in sound output usually the built-in speaker but possibly the mini-jack connector if a cable is connected. This is because remember the HDMI port has been turned off due to not detecting a signal from the display.
Now in theory when the display reappears you would expect it to switch back to it. Unfortunately this is not the case especially for the audio. (Even if your lucky and the video does resume going to the HDMI port.)
By far the best solution I have come across unfortunately requires spending some money to buy a device which will trick the Mac in to thinking the display is always connected and turned on even if it is not.
Note: Switching the input to the AV Receiver to a difference source (device) means the Mac mini will no longer have a connection via the AV Receiver to the projector and will therefore think it is disconnected/turned off.
The device in this case would be a Gefen HDMI Detective+ see http://www.gefen.com/kvm/ext-hdmi-edidp.jsp?prod_id=8005
You would first get this device to 'learn' the signal from the projector, this is then saved in to the HDMI Detective+, thereafter you no longer need to provide power to the HDMI Detective+ and even if the video cable is completely disconnected from the projector or AV Receiver it will still sending the signal to the Mac mini tricking it in to thinking the projector is still connected.
While your description implies the projector is not detecting the Mac it might equally be the Mac did not detect the projector and hence is not sending a signal the projector can detect either. Regardless this solution will also eliminate any delays caused by the Mac mini and projector having to renegotiate the resolution.