I suspect that the addition of your 751st stop is just crossing a threshold in the Network Analyst window after which it automatically collapses all the stops in order to save display space. The stops are still there and assigned to the correct routes, but you just can't view them in the Network Analyst window because there are too many.
Since you have sooooo many stops, it seems like it would make more sense for you to create a feature class of them using the editing tools before loading them into a Network Analysis layer. Your feature class could have a field called RouteName which you could easily edit in order to assign the stops to the correct route. Then, when you load the feature class as Stops in your route, just use field mapping to assign the RouteName field in your feature class to the RouteName property for the Stops. If you don't want to start over completely, just export your Stops as a feature class, add the rest of them, and then re-load them back into the NA layer.