[MMI Enterprises]

Wrong tip, worn tip, clogged downstreamer, major leak, clogged water filters, debri in pump check valves, muffed/cracked piston seals/packings, one cylinder of engine blown or not firing, etc, etc. ....In about that order.
Running a system that doesn't feed the bypass water back to larger tank and instead goes right back to pump in a small loop can overheat pump and mess up seals/packings. Always pull trigger every so often or have a temp based release valve off pump to prevent problem if your not routed to big tank.
Far as pump oil goes.. No not directly, yes low oil could fry yer pump but how high or how low does not effect pressure persay. Oil side is discrete from the water section.

ps-Update: Air entering the inlet plumbing to the pump or lack of supply water has to be added as likely cause due to learning that symptom fluctuates or presents only after trigger pull under pressure. So first thing to check is pump starvation and prime, filters, then valves.