Lots of fellow vegetarians here! Glad to see that!
Anyway I exercise all the time as a vegetarian and haven't noticed any changes compared to when I was eating a lot of meat.
I'm not sure what you mean about losing endurance, but I have two hypotheses:
The first is that you have not sufficiently replaced your protein intake. So you should simply eat more of the protein heavy things in a vegetarian diet, like beans, quinoa, or eggs/dairy. Munch on nuts throughout the day if you're really hardcore and need a lot of protein.
In my experience you will need about 1.5 to 2x as much mass of "proteins" that are non-meat as compared to meats. So this means that whereas I may have been satisfied with 1/4 plate of my Mediterranean meal being gyro meat, I know want 1/2 of it to be falafel.
However that may not be the case, the other possibility is a vitamin or mineral definiency, like iron or the B vitamins. To test the theory you can take a few supplements for a few days and see if you notice a change. If you do, great, but I don't recommend continuing to rely on pills, instead get what you need by eating far more fresh fruit and vegetables than you probably did before.
In fact, the best thing about being vegetarian in my experience has been the necessary increase in uncontroversially healthy food, like fresh broccoli or grapefruits or just whatever you want to eat.
So those are my ideas.
There is also the possibility of simple transition. It took my about a month to feel totally "normal" after I switched, between strange GI sensations and the odd feeling of weakness or fatigue. But that stuff disappeared after a while (likely more due to my increased skill at eating the right things rather than a GI adjustment), and afterwards I felt infinitely healthier in a bodily sense. Something about eating rice and beans instead of a cheeseburger makes the body feel more alive.
Anyway a good way to make the transition is to buy some of that fake meat stuff. Boca's chick'n patties are pretty tasty actually, especially the spiced ones. I also recommend trying out Quorn products. These are by no means a long term solution but can help tremendously as you adjust your diet habits.
One last thought is that you may want to transition into more, smaller meals rather than a few large ones, the former is more conducive to vegetarianism. If you are a huge carnivore, it is not inconceivable to eat a huge meal once in the day and go the rest of the day without feeling the need to eat much more. But as a vegetarian this is far less likely. It is usually better to reduce the sizes of your large meals and add in two or three fairly substantial snacks in between. This could help a lot with your bodily sensations of fatigue or whatever.
All in all I hope you'll keep giving vegetarianism a shot! The initial challenge excited me, but after a few weeks I started to miss meat, but after I got over that hump within about a month's time I found that being a vegetarian is much easier than one would think, and even more rewarding than its proponents might have you believe! The fringe benefits abound.
And if you can hold up long enough, your habits will eventually be reinforced by your GI tract, which will respond less than favorably to a sudden influx of meat, if you know what I mean by that euphemism. Keeps you honest in your weaker moments. Is the plate of barbeque really worth a night of the squirts? Not likely lol.