My BX23S loses power under load or after a bit of work. I changed the fuel filters, ran the fuel pump for 30 seconds, then started. Starts immediately, but when the mower is turned on, the power drops.
Go back to the fuel filter, and remove the line coming from the tank, and with the tank cap removed, blow through the fuel line, to clean any debris at the outlet. Also, check the fixture on the filter that this it attaches to, this would be where any debris too large to enter the filter will accumulate.