I had this problem when checking out on a Piper Arrow a couple of years ago. My ability to land just disappeared completely - to an extent that couldn't be explained by the few extra knots and a bit of extra weight compared to types I was used to.
My instructor figured out what the problem was - the runway we were using was directly into sun. We moved to a nearby airfield, and suddenly I was able to land. I'd have to check my logbook to confirm this, but I'm pretty sure I was signed off to solo the Arrow that evening.
As for landing in a tail-wind, there are two issues. First of all, what's the aircraft's tailwind limit? And second, is the field long enough? I took a PA18 into Tucson International a couple of years ago, and ATC directed me towards runway 11L for the departure. The wind was reported as 290/8kt. I guess an 8kt tailwind doesn't affect most of the aircraft which use the airfield (mainly airliners, with the odd F16 thrown in for good measure, and maybe a few spamcans) but there was no way I was going to try that in my Super Cub. ATC were extremely good about it, though, and gave me the option of either waiting while they changed runway (there were a few inbounds and a bit of circuit traffic that needed to be sorted out) or taking the crosswind runway instead, so I took the crosswind runway.
FFF
-------------