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[Tangled] Is Rapunzel immortal or self healing due to having the flower inside her?

I watched Tangled the other night and I wondered if Rapunzel is technically able to heal herself and stay young like her "adopted" mother? She is able to cry to heal Flynn Rider. Would she technically stay young or was it a one off?
gpt
Singing while her mother brushes her hair causes her mother to look young again, at least for a while since we see how old she looks even after a few weeks without her hair stroking treatment. 

However, we also see that the hair loses it's ability once cut, and it loses this ability all the way to its roots. 

Spoilers ahead for all you Tangled fans who are reading this but didn't watch the movie. 

Rapunzel's hair is completely cut, it all turns brown, so she has lost the ability to make people young by letting them brush her hair. From what we saw of her magic, stab saving tears, they've only worked once. That being said it's the only time we've seen her tears, so it's plausible that they work like this every time and that her tears became an incredibly precious healing commodity for the fatally wounded. 

What isn't clear is if she can use these tears herself or whether they do work all the time. 

If they do work all the time, and she can use them on herself, then she and Flynn became immortal monarchs together. Whether or not that is actually a happy ending is debatable since people would probably try to kidnap her to have an immortal source of immortality juice.