Question
Help me!  I continue to hear a drilling sound in my attic; mostly above the
master bedroom. I've also heard it as if it 'migrated' to the front bedroom, my
office.  It is driving me nuts.  My cat recently brought in a baby squirrel as a toy.
My neighborhood is filled with mature trees so the squrrel population is great.  
I've had two pest control companies come and they both say 'I'm stumped.' I've
GOT to do something about this. Last night it woke me (again) at 3:15 AM.  

Answer
Interesting. When you say, pest control companies do you mean, insect people? Or do you mean, two qualified and professional animal damage controllers? My hunch is you meant the former not the latter. My experience is that most pest control companies are very poor inspectors. Rarely do they climb ladders, inspecting roofs, crawl in attics, etc.
Second, I would suggest visiting http://icwdm.org  click on solutions then on damage identification. It is a page full of information on how a house should be inspected for wildlife problems. Then I would click on service vendors. REad our information how what to look for in a wildlife damage controller BEFORE you hire them.

As for your cat, keep him indoors. Free roaming cats pose an incredible risk to the environment and also can bring diseases home to their owners.
You can also call me at 402-472-8961  on Monday  9-4 CST if you want to talk through your situation. I am the webmaster for icwdm.org. By the way, all our information is free.