Whenever you captured an asteroid, a bug immediately occurs where you can no longer save the game, switch vessels, or go to the KSC. It turns out that this is caused by a contract bug. If you have a contract open to capture a specific class of asteroid and you fulfill that requirement, the save glitch will occur 100% of the time. However, if you cancel the contract (or simply don't take one at all), you can now save the game and progress after capturing an asteroid.
I've learned that;
-This bug only occurs if you have an active contract to capture an asteroid.
-The asteroid you capture MUST fulfill the contract classification requirement for the bug to trigger.
For example, if you have a contract to capture a 'B' class asteroid, but you capture an 'A' class instead, then the save bug will not trigger.
So basically, don't bother accepting asteroid contracts, because they'll break your game the moment you fulfill them. (At least for the Xbox version. I would like someone to test this out for the PS4).