Nothing lasts forever when it comes to hair because hair changes. It grows and you can cut it short. Therefore, specifically permanent hair straightening does not last forever. Whenever you get a perm in your hair, it changes your hair. It will either make it straight or curly depending on your hair and the type of perm you get.
However, strong chemicals are used for perms and straightening which are designed to last for months. That does not mean it will last forever. Depending on how fast your hair grows, that will show how long your permanent hair straightening will last.
If your hair grows fast, then the hair straightening treatment will probably last only a little while compared to if your hair grows slowly.