I did all my chemo without a port. I also had to have a blood test weekly. By the end I only had one good vein in action (which was getting pretty dodgy as well) and several times they called the phlebotomist to come and do the cannula. It's amazing where they can put the thing. One time it was half way up my forearm but on the outside!
The veins have been a problem for a while with more tests, contrast for bone scans etc. However, it seems they do repair. I had a blood test two weeks ago and it was up an gushing again.