Some stuff is too fast to just use downstrokes.
I will assume that you play metal, the technique isn't used very much outside of those genres. Then one thing to consider is string gauge. It might seem intuitive to have thick strings to pound away on, but a lot of metal players actually use quite thin strings. Then palm muting will be easier both up and down.
The next thing to consider is that almost all players are better at downpicking, since that is used more (and possibly since you have gravity working in your favour :)). In order to strengthen the upwards palm muting, alternate between playing only downstrokes and only upstrokes, in order to get an even sound. Try different combinations e.g. 4 down 4 up, 4 down 8 up, 2 down 2 up and finally 1 down 1 up. Like always, start slowly where you feel in control, and increase the speed as you build stamina.
As others pointed out, it is important to stay relaxed, otherwise you will wear out. The motion should mainly be in your wrist. It's common to tighten up and use the entire forearm when tempo's reach the outer limits of ones ability.
Using a quite heavy and pointed pick is recommended for precision. I personally use Dunlop Jazz III, but there are a lot of different types and shapes out there.