New points you earn are available for transfer at the end of your billing cycle. So if your cycle end Mar 25, you can call on Mar. 26 and have those points transferred to your card. You can also transfer points on the website.
We were on our trip and decided we wanted to add points to our gift card. We just called and had what we had available transferred. So long as you have points you can transfer them!
I do believe there is a $10 minimum to transfer (it is a $20 minimum the first time you order the card, then $10 minimum each time you add to it). Other than that, once the billing cycle closes you should be able to transfer whatever you want over.