Personally, I would play the Ab twice (once for the chord, once for the dotted minim/half note) but then hold it down after playing it for the second time. The second Ab has its stem upwards which signifies that it's a different voice - and from what I can see, it's part of the melody of the piece, so it's a pretty important note.
Different voices need to each have their notes' lengths add up to one bar. So, this is okay.
Because each voice adds up to 4 crotchets/quarter notes in that bar (you can tell which voice is which by looking at the different directions of the stems).
However, this isn't:
You'd need to add a rest before that note to make it okay:
This applies to situations where the notes cross over:
It's not obvious what to do, but in the context given, playing the Ab twice is probably the best thing to do.