A couple suggestions on starting the grill. First, if it is a windy day, that can cause problems lighting the grill. If the gas is being blown out of the ignition area while trying to light it, it won't light very reliably. Also, the burner might not be full enough to push much gas out of the igniter holes by the igniter. This is especially a possibility if you routinely turn your tank off after every cook. The line can empty of pressure before your next cook and it takes a couple seconds for the gas to fill the line back up with LP after the valve is open.
Now for the disclaimer. This is not the preferred or officially recommended way to light a grill, but this is how I routinely light my grills. I leave the lid down, turn gas on at the tank, then the first valve. I wait about 2-3 seconds for gas to start flowing and then hit the button. The lid down helps prevent the wind causing issues. These grills can actually flame out after being lit on windy days, so wind playing heck with the gas near the igniter is definitely as possibility.