What you've described points to an issue with your general configuration of CUCM for CWMS integration.
Unless you have a 2000 user system (or 50, 250, 800 users with High Availability), you most likely have 1x Load balancing point and 1x Application point on your Admin VM (Administration > Settings > Audio). Both of these points will use the same IP address - Admin VM IP address.
On your CUCM, you need to ensure you have 2 SIP Trunk Security Profiles (one for Load Balancer - port 5060, and one for Application point - port 5062).
Then you need to have two SIP trunks, configured the same way, but one (Load balancing) will have Destination port 5060, and use SIP Trunks Security Profile with 5060 port, while the other SIP trunk (Application point) will have Destination port 5062 and use SIP Trunks Security Profile with 5062 port.
You will need to create a SIP Route Pattern that will be IP based and point to Application Point SIP Trunk. You will also assign a partition to this SIP Route Pattern. You need to ensure that in the two SIP trunks (Load balancing and Application point), in Re-routing CSS configuration, you enter CSS that contains the partition assigned to SIP Route Pattern.
Also, in both SIP trunks, in Incoming Calls section, you will have to specify CSS that allows you to reach out phones you want to allow to be outdialed from CWMS (this CSS is used for call backs from CWMS)
Finally, you will create a Route Pattern that points to Load balancing SIP trunk.
You can find official document here: http://www.cisco.com/c/en/us/td/docs/collaboration/CWMS/2_5/Planning_Guide/Planning_Guide/Planning_Guide_chapter_0111.html
Now, to explain what happens when you dial in compared to call back.
1. When you dial in the access number, it uses Route Pattern and Load Balancing SIP trunk (port 5060) to reach CWMS.
2. At that time, the call is setup and CWMS plays the prompts.
3. You then enter Meeting # (or in case of Blast Dial meeting you enter PIN).
4. At this time, CWMS checks to see on what Application point this meeting is hosted (this is the logic inherited from larger deployments with many application points; in 50, 250, and 800 user systems without HA there is only one)
5. CWMS then uses SIP Route Pattern to REFER the call back to CUCM and then back to CWMS using Application Point SIP trunk and then the caller is connected to the meeting.
Hence, if your call gets dropped after entering regular Meeting number or Blast Dial Meeting PIN, that means that this REFER failed due to some misconfiguration on CUCM side (either SIP trunks are not configured properly (no re-routing CSS or is not including partition of SIP route pattern), SIP route pattern is missing something, or something similar).
I hope this will be of help.