If you use Rogaine for traction alopecia, you wouldn't have to use the product for life once the hair grows back—correct?

No, you would need to use Rogaine to keep the results. I suggest seeing a hair loss expert now to evaluate and go over your condition and provide you information about your best treatment options. There are great non-invasive options like prp/progesterone and/or hair transplantation. See an expert. Best, Dr. Emer

I agree with Dr. Donovan regarding his assessment of traction alopecia. I would add that sometimes traction alopecia occurs as multifactorial disease with  female pattern hair loss. In this case, one would need to continue the minoxidil.PRPHAIRMD.COM 

Depending upon the duration of the damage, your hair may not grow back fully. The hair which is lost may be replaced by grafting techniques however. Seek consultation with a board certified plastic surgeon specializing in these treatments. Best of luck.

To some extent yes. It depends on the severity of the alopecia, but rogaine can at least in part help to undo the effects of it. However in most cases it is impossible to return the follicles back to their original healthy state completely. But yes, if you stop rogaine later on and treat your hair more gently it probably won't regress. These are all generalizations though and so it's possible for any specific case that some or all of these assumptions aren't true- a hair loss specialist can help determine if you fall into that category.

You are correct - in part. If your traction alopecia has gone on "too long" (meaning many months), the hair follicle CANNOT completely heal. Therefore it can not completely regrow. However, if the traction has gone on a few weeks, the potential is there for complete healing. IN this case you are right, you can stop Rogaine and the hair will still keep growing. Traction alopecia is often not completely regrowable if the damage has gone on too long.

Minoxidil (Rogaine) does not work to reverse traction alopecia. At most you might get some fine hairs growing

If you have had traction alopecia for a while, you may not have conplete recovery after using rogaine. However if you use rogaine for a while and gain some hair back, those hairs nost probably will remain even if you stop using rogaine.