Chainsaw Repair

That is a tough one.

Like killians stated could be the filter.   Have them try it with a full tank of fuel.   
Pull the starter cover off and check the wiring to make sure when the saw is on its side nothing is shorting.
Get a flash light and check the rubber intake boot carefully.   
Pressure test with saw sitting on its side.

The bottom line is that something is changing when the saw is put on its side.

Does the saw instantly die or does it try to run and then eventually die.

If it dies instantly I would think ignition problem.

If it tries to run and then dies I would think fuel problem or air leak.