Got owned yesterday heads up

[Indiana]

To start, I play lots of stars heads up matches and do very well. However, lately I have been getting owned at the end of tournaments, especially when it gets to heads up in sattelites and such. The difference for me is that heads up tournaments start with deep stacks and low blinds so I can easily outwit the opponent and take him down, whereas at the end of the tourney I am facing a very high blind and aggressive opponent. Last night I was getting raised almost every hand before the flop. Blinds were 300/600 and I had only 8K and he had like 20K. Anyway, I was owned and he grinded me down. This situation repeated itself in 4 satts.

Any help with how to deal with this endgame situation?

Indy