Can the port in my computer be replaced?

Only by replacing the motherboard to which it is soldered.

"I've had to hold the DisplayPort to VGA adapter a certain way to make sure it connects when I initially put it in, but now it's not detecting it at all. I'm a teacher and use my laptop every day to project presentations etc."

Can you post a very close up picture of the display port?

You'd better make a Genius Bar appointment and ask them about the replacement cost.

OK so that port shows the amount of use it's had.

Do you have a competent tech at the school where you work?

You could actually do the analysis. We need to look inside the port itself (socket) and the plug you're using for damage to the conductors. Whether they're damaged or missing. If they all look clean, not deformed/displaced and not missing then the damage will be on the logic board itself. It will be a broken solder connection. There are quite a few of them and they're tiny. The logic board will have to come out and the solder connections examined.

I have repaired things like this and it will take someone who can do near micro soldering to do the repair. This was at a charter school doing work for teachers and the kids who went there.

If that's not the problem or you can't find someone who can do the repair then you will have to replace the logic board as Allan says. You can ask Apple but I'm not sure they'd work on it.

Where are you located?

Clean up the port by cotton bud with alcohol would works.