I think prolong also has an implication or suggestion that the increase is somehow extra, beyond what was originally planned, and often done when you are already in that meeting, visit, or whatever.
For example:
The discussions were scheduled to last two hours, but we had to prolong the meeting because some participants talked too much.
Janet and John prolonged their visit to England because Janet injured her back.
BUT:
The conference organizing committee decided to lengthen next year's plenary session to accommodate more discussion.
The government has announced that statutory holidays will be increased (NOT prolonged) by five days per annum from 2020.