I finally solved both issue, after countless hours of digging:
The “No available channels” error:
This was caused by selecting “Italy” as the country in the wireless settings. When using this setting, only certain DFS-compliant frequencies (mainly UNII-2 and UNII-2e) are allowed. If your frequency list includes channels not permitted in Italy (like UNII-1 or UNII-3), the AP won’t find available channels.
I’ve set a frequency list that includes only allowed channels, or use “regulatory-domain” to let Capsman automatically select compliant ones.
I know that it could have been easier to not specify all the available bands manually and let the capsman to handle those.
About the sudden disconnection when enabling the second AP: I had duplicated the configuration from the first AP to the second, which also copied the bridge settings. In particular, the line
/interface bridge add admin-mac=…
was forcing both APs to use the same MAC address for their bridge interfaces.
Winbox showed the same Mac address for both units and both APs received the same IP when DHCP is enabled. This of course causes random disconnections and instability. I removed and recreated the bridge on both devices without setting a static admin-mac. After that, everything worked flawlessly.
A similar thread that helped me to fix this issue is:
http://forum.mikrotik.com/t/two-cap-same-ip/156678/1
Hope this helps others facing similar issues!