The usual suspects of an early-closing linkup are two:
1. It might be an advanced setting regarding the maximum number of links in total. This setting automatically closes the linkup when the total number of links reaches the set number.
If you have set this to something small, then the linkup will close.
2. Another possibility would be that the time was not set correctly and the linkup closed in e.g. 11 AM instead of 11 PM. For midnight, the correct time would be 12 AM and noon would be 12 PM.
Note: Trial and free accounts are only allowed up to 50 links per linkup.