If you are planning on selling your property, you will need to order new title insurance. The old policy is unnecessary and you can use any local title company that you wish. All title companies do the same type of title search so there is no worry about a "lapse" of coverage.
Simon, I thought the same thing regarding American Title in Houston, but after speaking with them earlier in the week they confirmed they are unaffiliated with American Title that was in Dallas in the 1990s.
Kim, my next call will be to the Texas Dept of Insurance to find out where my policy landed.