I usually use my white tea leaves for multiple infusions without any problems. I use an infuser basket like the black one here:
You'll taste it if the leaves have stewed. Trust me. Generally, though, loose leaf is better, if you're drinking actual tea. Good loose-leaf tea can be spendy, but I've found that if you're good at preparing it, it's worth it. When it comes to herbal tisanes, I still like bags a lot.
I've also discovered that Mighty Leaf bagged teas can be infused three times before the flavor goes kaput. You pay more for Mighty Leaf teas, but they're really superior bagged teas--the quality of loose-leaf in silk sachets.