You don't necessarily have to delete apps, but some apps as mentioned run background tasks and are not blockable in the 'background tasks' settings page. And the deal seems to be that you can't have too many running or the system gets overloaded and stops working completely or unreliably. What worked for me and has since, is go into each app individually that you have installed and make sure any that have live tiles and/or background tasks turned on in their settings are disabled even if you have them blocked at the background tasks settings page. Essentially you have your 5 on that show enabled and a bunch of others that don't allow you to block them from that page so you end up with too many running unknowingly. Hope this helps and feel free to ask for clarification if needed.
Edit: Oh and the best 'guess' right now among some people is around 15 or so apps running agents (Live Tiles, Background Tasks), but that is a total guess and could be higher. However I would shoot for that number to get it fixed and once working, then slowly add to it until it stops working properly then you have the number that works for your device if it's not a hard cap for all.