1) Maintaining an acceleration requires fuel.

2) Even though you don't observe yourself moving at increasing speeds, you do observe the rest of the universe moving at increasing speeds. This means that small particles impacting your ship will hit it with increasing energy.

I'm being accelerated at 1g right now and I'm about 40...so in another decade or so I should be able to get to anywhere in the universe!

Jokes aside, there's no fuel source we know of that would allow a ship to accelerate continuously for 50 years at 1g.