My experience with Gyft may differ from others, but somewhere around $2k seems to be their limit for BTC transactions. Once you get near it, they will want a new payment method. You can setup a new account and continue, from my experience, but it requires another Facebook (or G+ I believe) and about the only card they carry that eGifter doesn't is Walmart cards.

However, one $250 walmart card I bought from Gyft didn't work when the person I gave it to tried it at the store. They refunded 48 hours later, then changed all Walmart cards to $25 max.

With eGifter, no issues. I'm well into the 5 digit area on gift cards with them. Their CEO seems like a cool guy who was nice enough to send (apparently everyone who used BTC in 2016) $25 and some insider points (which are a bonus discount on your next card) the other day.