Hello Juan
Just like any other protocol communicating on the network, BGP requires the appropriate MTU sizes to be set in order for communication to occur successfully. If you have to tune the MTU value to get BGP to work then it seems that BGP is sending IP packets larger than the interface MTU that have the DF set to 1, which means to not fragment. By adjusting the (IP or interface MTU) of the subinterface, you are essentially adjusting the allowable MTUs such that the IP MTU will be small enough to fit into the interface MTU. It also depends on what other protocols you are running such as QinQ, tunneling or encryption that may add overhead to a packet or frame making it larger than the allowable MTU.
For more about MTU sizes, take a look at this lesson:
I hope this has been helpful!
Laz