My 07 Tacoma had the frame replaced by Toyota because it rusted. Can I expect the new frame to fail too?

No.

Not for a long time

Toyota will have replaced the frame because they accepted there was a defect in them that caused them to rust out too quickly. I don't know the details, but probably something like, they should have sprayed some zinc based paint on them first, and they missed that step.

They aren't silly enough to replace a part with an equally faulty part, because they would still be liable when that rusted out. Remember they have acknowledged it was a faulty part.

BTW, it's nothing to do with "Mexican Steel". Higher grade steels may rust just as easily. It's related to the salt used on some US roads. In other parts of the world (Maybe Japan?) the frame would have lasted normally, or in Arizona it would have been great. But they have acknowledged that the primer / paint used wasn't up to the job in the market they were sold in.

Very doubtful that Toyota would spend millions of dollars and replace the frame with one that has the same rust characteristics and the cause of all this expense. In a word _NO Worries.