My hubs veins used to roll. It was always done in his right arm; never his left. For some reason they could not get an IV started in the left. He would get admitted over night- thankfully only 3 times- every 22 days. I asked they do his left arm since he is right handed. I've been in the hospital before with a line in my right- it's not pleasant needing to use the bathroom.
My hub is fine almost 12 months out.
My dads veins were trashed & he had a PICC line. For some reason they still had to stick him; wish I could remember why- he fought 8 months, I don't recall his veins recovering. His chemo was radical due to it being a clinical trial- what ever they gave him killed his heart & lungs.
I would imagine it would depend on the person & what chemo is used.