WMM (http://en.wikipedia.org/wiki/Wireless_Multimedia_Extensions) is a Quality of Service (QoS) feature which while it can be implemented with earlier protocols (b) seems to only be implemented in the N version of Wi-Fi. As in the n of 802.11agn. Each letter refers to a different radio mechanism. WMM also has a power saving feature specified in the standard 802.11e which is causing the problem. Something along the lines of the router telling the device after every transmission: OK I have sent you everything, you can now power down your wi-fi. This appears to happen every few seconds so the device experiences poor connectivity. The older protocols using 2.4 GHz don't implement WMM, it is only implemented with N which is why people experience the problem going away when they switch to 2.4 GHz.
N is of course considerably faster so if you can make it work and switch to N only you are in the best possible position.
So the problem is an interaction between specific implementations of 802.11e power management on switches supporting WMM power management as part of their implementation of N. If you experience the problem try each of the following in turn, moving to the next option only if, after testing, the problem persists:
1) Upgrade the software on your apple device
2) Upgrade the firmware of the access point
3) Look for an obscure setting in the access point's admin pages under Wi-Fi which lets you disable WMM Power Management and disable it
4) Look for an obscure setting in the access point's admin pages under Wi-Fi which lets you disable WMM completely and disable it
5) Look for a setting in the access point's admin pages under Wi-Fi which lets you disable 802.11n and disable it.
6) Look for a setting in the access point's admin pages under Wi-Fi which lets you restrict it to 2.4 GHz
7) Replace the access point with a later different model.
The admin pages will generally be on 192.168.1.1 and have a very simple password, often written on a label on the router, or contained in the manual found on the internet.