Go to the Park web site. Look up front derailleur adjustment. Disconnect your shift cable and start from the very beginning.

My suspicion is that the problem is in the LOW limit screw adjustment. If that's off, you're starting with a little too much cable tension to hold the chain on the small chainring. If your chain tension is a little too high, your STI, which pulls the same amount of cable every time, is pulling the chain right over the chainring.