You may be running out of energy (mental or physical) on the back nine.  Competitive golf really takes a lot of focus -you might try drinking water or a watered down sports drink all through the round and then fuel up with a banana or some light protein/carb snack at the turn. 

I am usually the same way if I dont get out well before the round and get to the range.  Takes a while to get nice and warmed up, loose, find your swing.  Try getting out way before your round to get warmed up and see how that works. 

I struggled with the same issue. Last year in my state Amateur stroke play portion I was a combined 11 over on my first nines, and 1 over on my second nines.  However, this year I really tried to start much better.  Some of the things I changed: my warmup routine, my mentality, and what I ate for breakfast.  

For my warmup, I used to go straight to the range and then to putt and chip, and I think that I was no longer warmed up when I got to the tee.  I changes it so that I now spend ~30 min putting and chipping, ~30 min at range, then I putt and chip until tee time.  

For my mentality, I used to go out very nervous and wanting to go out and make some birdies, but now I really try to play my first three or so holes super conservatively, 3 wood off the tee, and then aim for center of green, then cautiously two putt.  

Finally, for breakfast, I used to eat a fairly fatty breakfast, and I would often feel bloated, I now try to eat a healthy breakfast.

Hope all these things that improved my starting can help you.

Spend more time warming up your short game and putter.  Also as part of your warm up, play the first three holes in your head.  Remember that on the first tee, you should have no expectations except to be mentally prepared for each shot and to have fun (courtesy: Bob Rotella).  Anything you can do to make the first hole feel like the fourth hole will help.

Today I played in the quarter final match play game and won against my opponent by only 1 and this happened on the 18th hole. I began the match playing well and was +4 on the front 9 but after lightning threat and a rain delay, it was soon even by the 14th. Looking back on it I noticed I was starting to pay closer attention to my opponent's game and less on my own when I started to lose holes. I have to say it was a mental grind trying to get my focus back on my own game and on my next shot. The match went up and down for the next 4 holes but I think I was very lucky to get the win. I'll definitely take on Cathi's advice to take a lack of energy out of the equation but does anyone have any advice as to how to mentally overcome a change in momentum and regain the confidence?

Its all in your head I'm a junior competitive golfer and lemme tell ya, as soon as your mental game starts to fail, you play terrible and in my case for about 3 months in the mid 70's so im kind of in a slump but when it gets sharp again it'll kick back into gear.  Try eating your way around the course take a bite of something on every teebox and drink lots of water. Otherwise stick to your routine and play your own game dont worry about anyone else.