After some testing the Vector Prime community found that, for some strange reason it does matter which menu you use to load a saved game. In fact, the crashes related to loading a saved game might have to do with the main menu background as well.
For now, here is a little hint that *might* work for you: if you are having trouble loading your saved game from the main menu, try starting a skirmish game (your best option is to use settings similar to those you had in the save), then when the game starts, press ESC. Using the in-game menu, navigate to Load/Save and try to load your saved file.
Please note that we have little idea on why some saved games do not load. Take this short tutorial as an advice and let's hope for the best.
Edit 1: It has been confirmed that this is not a 100% solution for your saved games. We are looking into ships with dual hardpoint assignments to see if they might be the cause for this error.