The short answer is yes; you can repair power washers. However, you really need to ask if they should be repaired.
A high-quality power washer that costs you quite a bit of money can be repaired and should be repaired. This will prolong the life of your washer, meaning your purchase and repair costs offer over 10 years of power washing.
But there are also much cheaper pressure washers available. While you can also repair the cheaper models, sometimes the cost of a few repairs will equal what could have bought you a new power washer.
This will also depend on the repair that is required for your washer. But be aware of how much your washer costs and what repairs you are faced with.