"Hold the line" is an expression meaning to maintain your existing position, which in this case is the singer telling a girl to be patient and stay with their relationship.
The saying also has a more literal meaning, however, which is how David Paich came up with the title. "Hold the line" is what you tell someone on the phone if you want to put them on hold while you're taking another call. This is typical in workplaces, but in the days before cell phones, some households (especially ones with teenagers) also had multiple phone lines coming in and could put callers on hold. Paich lived in one such household.
In his 2015 Songfacts interview
, Paich said: "When I was in high school, all of a sudden the phone started ringing off the hook, and I had a situation where I was at the dinner table and I had three girls all call at the same time, so all the lights were flashing. I was kind of juggling girlfriends, and that's how that came about."