My husband and I are relocating to Cozumel, Quintana Roo, Mexico soon. We will be traveling on our tourist visa, so that we may stay up to 180 days before being required to return. I really do not want to purchase round trip tickets, since we are not exactly sure when we will be returning. Will traveling on one way tickets be a problem with either American Airlines or with Immigration in Cozumel? I have not been able to get an answer from AA.
Thank you.

I can't recall ever having to show my return ticket to immigrations when entering Mexico?? You just show your passport and the immigration/tourist card form you've filled out.

not a problem. for all AA or INM know, you're flying in and busing/driving out.

Since retiring in 2004 I have not purchased a round trip ticket. Never a problem

Just to be sure - are we talking to a US citizen? Canadian? other? May make a difference. Suggest you surf the sites for the Mexican consulate in your area. Most times this has the answer, although sometimes it may be a bit hard to mine out of all the bureaucratese

Not a problem entering Mexico, but entering the USA is another matter entirely.

We have been questioned a few times by the airlines before getting our temp residence visas(we're now applying for permanent status) because we never purchase RT tickets.

First off ask the airline if it's one of their requirements - they are legally not supposed to enforce this requirement but some do.
Here's what we did one time prior to getting our temp res visa -
I made a reservation with an airline that we weren't traveling with and then cancelled it to show that we had return flights. No one questioned the paperwork showing the return flight info copied on a flight itinerary paper.
In our case it's always been that the airline agent goes through the motion of making it look like they are checking for return flights.

I'm told that return flights increase their revenue and helps them plan and set pricing.
Have your visa in hand, a copy of your Mx address/electric bill or something showing that your intent is to live in MX and for extra insurance some sort of flight itinerary.

"Not a problem entering Mexico, but entering the USA is another matter entirely."

How so?

If you are from Canada, do not be concerned, as we often leave on a one way to return on on an unknown date... We have also extended and also shortened our departure date, no problem, we just had to pay a penalty with the airline is all !

Thank you for all the helpful information. Really appreciate.