What is going on with my lawn mower?

I have a push lawn mower (gasoline) that is barely two years old and works fine, except for starting it up. I have to constantly press the primer button until it finally stays running.

This is what happens: I’ll press the primer three times, pull the cord and it will barely start up and then stop. Press the primer three more times, it will start up for a few more seconds then stop. Press the primer three MORE times, it start for about 5 more seconds and then stop. I do this until it finally stays on. Which is between 5 to 7 times.

I know this is probably bad for the mower and could flood the engine, but it’s the only way to get it running. One winter, I did leave some gas in it accidentally, but other than that it has had no other problems.

Also, I did clean the filter and the oil is fine.

What can I do to fix this problem? What can I check or clean? Anyone else have a similar issue with theirs?