I'm not certain if absence actually makes the heart grow fonder. However I believe absence can cause one to 'romanticize the past'.
Even when people leave abusive relationships they're often prone to only remember the 'good times' when considering reuniting with an ex. On the other hand if things were great when you were together it's natural for one to miss not having that person around and look forward to reuniting. Like having ice cream after going without it.
However if one was tired or bored with their significant other I doubt their absence causes the heart to grow fonder but instead gives them a "second wind" to cope better. The absence was needed to keep them from the breaking point like taking a vacation from work.