Could I keep my deed with the Notary Public??, that way it will be safe.

No, I recommend you to pick it up,  because in the event something happen to the Notary Public, all the documents will be taken to Guadalajara, and it will be very hard for you to get your document back. Cheers.

Ask the notary if this raises any legal issues. When I picked up my deed the notary made a comment about how it was better for me to keep it in my possession (even if in a safety box). I forget the legal reasons he mentioned but the upshot was, less delays in getting the documents released after my death.

You can get a certified copy from the property registry office for 350 to 450 pesos if you did have it then lost it.

It is important to pick up the POA, WILL or DEED you made in a Notary Public. The point here is, to have the paper handy when needed; I recommend you to scan it and keep it in an electronic file.
If by any chance you loose your property title, (deed) you can always get a certify copy of Public Registry, but in order to do that, you have to have the page of the Public Registry, that is why it is necessary to scan it. If you do not have it, they can make a search, but it will cost you a little bit more.
Talking about losing a WILL, you have to go to the Notary Public and ask him to prepare a second testimony (by written), It will cost you around $1,000.00 pesos.
If you lose a POA, it depends the kind of POA, the grantor need to talk with the Notary Public and he will let him know if it is possible to make a second testimony or if it is necessary to make a new one.
Cheers!