Without any answer from Cisco, I've made following changes:

1/ installed and Apple Airport Extreme to solve connection issues.
Installation and connection piece of cake.

2/ could get the WAP stable with iPhone by changing following settings:

- disabled bonjour functionality

- set a static channel for 2.4Ghz after checking frequency usage.
  make sure that multiple antenna's have minimum overlap in channel usage.

Option 1 would be nice but I need a POE access point as I have no poweroutlet available at the AP locations, but yes crossed my mind.

Option 2

I allready did this, found this option on this forum, but did not help a lot, still unstable behaviour.

And Cisco is still not answering ...

In short yes been there done that. Tried 5Ghz only, 2,4Ghz only both, symoultanious radios on on same SSID and both on on different SSID's  (and yes deleted the old associations every time on the devices.) Behaviour kept exactly the same in all situations.

In remark to the 5ghz coverage of these AP's, this is quite disappointing and not sufficient. I have tried 2,4 only and had an acceptable coverage.

Also did a site survey before we choose the most optimal channels in both the 2,4 and 5 Ghz ranges.

Long story short, from my perspective either I am doing something extremely wrong here, or this Access Point has some serious issues. Judiging by the amount of complaints and the lack of response by Cisco I am putting my money on option 2.
But again I am allways open for suggestions, as I still keep the option open that it might be a stupid mistake by me.

Sorry to hear that.  I have never used those specific APs, but have fought with wireless issues with Apple devices and Cisco.  Most always come back to 2.4GHz.  5GHz issues typically deal with range.  2.4GHz has much great ability to drive through walls, cubicles, and other man make material.  Because of this, 5GHz only deployments typically require greater density of APs in building, unless the rooms are large and open where the radios do not have to pass through much to get to the computers they serve.  On the other hand, 2.4GHz can be a nightmare where one or more of those previously mentioned interfering devices exist or there is high user to radio density. Have you tried something such as the free WiFi Analyzer app on Android to do you own site survey during peak business hours?  This may not be relevant to you depending on your deployment. I have a few of my offices that are crammed in the middle of high rise buildings, with other businesses WiFi above and below them.  That coupled with their own WiFi emitters can be a nightmare!  Good luck and hope you find a workable solution.  

I will open a TAC case (if possible) for this as Cisco will not reply to this, and the replies I read in the small business section of this site where not realy great.

I bought these access points as a try out in a small installation in someone's home.

Normaly I administrate a bit bigger network with Enterprise level access points and wifi controllers all cisco based.

Never EVER had an issue with Iphones, not to mention that we ever had to disable the automatic channel switching or other services. Having Wifi networks with over 200 access points on some locations I think I have an idea what I am doing here. Then again, I have been proven wrong sometimes :)

To mee it seems that this hard- and software is no way near the level I am used to and it is just a cheap and buggy solluition with a cisco sticker on it. I am really dissapointend.

Let me know if they come up with a fix.  I too have never used their SMB line of APs, so am interested.  I have had issues with Apple products, but again those all dealt with 2.4GHz channel issues where no clean channels where available and 5GHz needed to be used.  One issue was that older Apple products such as pre-4S iPhones had no 5GHz radio support and iOS and the other was OS-X will always use 2.4GHz over 5 regardless of RSSI and SNR.  I am not sure why the latter problem seemed to be fixed by using AirPort wireless products, but it actually does.  I can only assume Apple uses custom extensions for WiFi channel and band selection vs CCX true extension use.  That is just a guess, but that always seemed to be an Apple specific wireless problem that wasn't specific to Cisco APs - seen also when deploying other wireless vendor equipment. 

Too bad, I am not able to create a TAC case .. contact your supplier Cisco states .. bottom line .. DO NOT BUY THESE ACCESS POINTS ..

Service is non existent,

Firmware updates rare (only 1 available)

And they do not coorperate well with one of the worlds most popular smartphone ..

Well done Cisco .. well done ..

I think we all get stuck with these WAP's.

Let me admit that the coverage range of an AirPort Extreme and the WAP371 are identical.
Main difference, using the AirPort all is working fine and fast!

I've recovered my WAP371 in an outer corner to ensure coverage and with the made settings is working for internet and small tasks.
Not for the serious work.

As said, getting in touch with Cisco is impossible.
Not professional. But as you see and read, you lost your money.

When Cisco acquired Linksys and rolled it out to satisfy a small business offering, they didn't offer the standard Cisco TAC support offering. Their womb staffing is basically a third party wing of high does not go through the same employee scrutiny. I remember talking a support tech through getting a serial console session into a switch. He and his manager had only ever used the web interface.....