Several people have been confused by this issue so I thought I would post the answer here:

Buildings check their road access to determine what type of transfer offer to put out (eg global or local park request). If they put out a global request but normal garbage trucks can't reach them then they wont have their garbage collected.

A way to check this is if you look at the "Transfers" tab for one of the buildings that isn't being serviced you will probably see that it is putting out a Garbage request with a "Park" value of 0 (global request) instead of a number greater than 0 which is the park request.

In the linked image you can see the building is putting out a Mail offer with a Park number 106. Service Point buildings only respond to requests that have the same park identifier as the pedestrian zone they are currently in.

Pedestrian Zone Request[i.imgur.com]

If you see a global request instead of a local one, then here are some things to check:

• Make sure you check the road in front of the building is covered by the pedestrian zone.
  
• Make sure that the road is actually a pedestrian zone road from the "Parks & Plazas" section. You can tell if the road is incorrect if you have bollards at the intersection.