Because of the low inventory, population growth, and immigration to Texas from
other states it makes rentals scarce.
During the scarce times, investors will raise rents and impose bigger restrictions such as no pets.
Good luck and keep after it....hopefully you will find what you need.
Another idea is to get outside the city. Sometimes prices can go down there.
Read the above link for a short answer to the Coming "Rental Boom"...
Here's another Trulia Q & A: http://www.trulia.com/voices/Home_Buying/BIGGEST_Rental_Boom
You may want to begin also looking for "Rent to Own" or "Lease Option" properties. As these may well soon be taking over the Market... (For many reasons!)
Rent is now becoming more expensive then a Mortgage in many areas and as the supply and demand increases, so does the Rent. While also lowering availabilty...
Best of Luck to you and your Family!
Lynn911 Dallas Realtor & Consultant, Loan Officer, Credit Repair Advisor
The Michael Group - Dallas Business Journal Top Ranked Realtors
Good luck with your search. It looks like Aaron may be able to help you out.
-Aaron Nelson, REALTOR
Dierschke & Dierschke Realtors