I'd imagine anyone, even the best player out there given 2$ could wind up losing the br if that's all it was......good or bad variance will take its toll and starting from just small freeroll winnings you need to hit a good swing early to be able to get a head start on the build to withstand variance.

Obv improvement is always a must, but something else for thought is perhaps to build from freerolls and don't play with the $ until you have a small br built up, I am doing something similar with the po freerolls on acr whereby I have no plans on playing with the $ until I have at least 20$ so 10bi for 2nl cash games which should certainly be a start to build a br....just food for thought to the OP as it will also allow you to play some, step back review the hands you played post hands you want feedback on and improve your game while still being able to play and not have to wait for the next freeroll cash.

Think about it this way, what provides the best opportunity to improve. 20 one time shots at playing, or 20 buyins that allow you to lose a couple review and see where you could have gone wrong and then improve on the mistakes without having to wait for the next freeroll cash......experience means a lot and consistently playing for real $$ will bring more experience than playing freerolls and only playing real $$$ when you happen to cash a freeroll.

Good Luck.