Prius intermittently not accelerating

First, welcome to PriusChat. To get things rolling, I'll take a guess and say it sounds like limp mode is being activated. This may happen when the traction battery gets too warm to charge. What does the state of charge (SOC) indicator on the dashboard say? The low end torque of the hybrid system is provided by the electric motor(s) which will not operate properly with a overheating traction battery. It is advisable to use A/C during these blistering summer months to protect the traction battery from overheating. Did you take the vehicle to a Toyota dealer to get any codes read? The hybrid system codes are usually not accessible without a Techstream reader. If the ICE (internal combustion engine) runs then it probably isn't fuel system related.

 

As AzWxGuy stated, the Prius launches from a stop with electric power, not ICE. Limp mode is designed to protect the synergy drive when the traction battery is not up to snuff. No mechanic will tear into anything without any codes. With 220K miles on the traction battery, I think it's time to have its health checked. You can have the traction battery tested for performance, which can identify individual cells that may or may not be performing to spec. If NiMH, you can replace individual cells. Not sure about Li-Ion. There are aftermarket shops that specialize in rehabilitating Prius NiMH traction battery packs. You can probably give them your traction battery pack and they will give you one that has been rehab'd. You'll get a credit for the pack you give them.

One final thing, make sure the traction battery venting in front of the rear seats is clear of obstructions and filter is not clogged. Perhaps put someone in the back seat when it's really hot and determine if the cooling fan is operating. You should hear it blowing.

Maybe tear into the entire traction battery area under the rear seat / storage floor and inspect the entire traction battery for dirt / debris that may contribute to overheating. There's probably YouTube videos on accessing the Prius traction battery.

 

Find another mechanic!
There's a test port on the fuel rail. A mechanic just needs to screw a fuel pressure gauge to it to determine if the fuel pump is operating to specifications. Besides, if you had a fuel pump issue the car would seem like it's running out of gas on the highway every-time you try to accelerate.
More than likely it's your traction battery pack being low. Switch your MID over to one of the traction battery display icon and note battery status when this happens. Replace your battery inlet filters, clean out the cooling pathways, lube the fans, and check the exhaust pathways behind your rear tires under the bumper wells. .

Hope this helps....