I can only make a guess on this one.
Perhaps, with the longrod fitted, the bow is a little too heavy in the hand or slightly off balance, causing you to struggle that little bit on the draw, causing the arrows to bounce on /off the rest.
Just to clarify, when the arrow comes off, had you noticed the blade bouncing up and down just before; did it sound like it was rattling?
Without the longrod, was the arrow running smoothly on the rest, and was the rest fairly still during the draw?
There is sometimes a fine line between falling off and staying on. My rest is worse with carbon arrows as they don't slide so smoothly.
I can adjust the springiness of my rest, and a slight change can make all the difference, too.
I would examine the rest to see there is no roughness at the contact points with the arrow. I know that if there is any roughness it will still be there without the longrod, but better to eliminate it if there is any.
Another thing could be nock point too tight. That can create a situation that makes the arrow lift on the draw.
As for keeping on with the longrod. I would watch what happens when you draw with and without the rod. See if anything shows up in the way you draw the bow. It might just require you to draw in the same way you do without the rod.( fitting a longrod can sometimes produce a slightly different draw even though you don't deliberately change it.)
With the rod you may start with the rod resting on the ground, without it the bow is held differently.
Another thing worth doing is reduce the poundage and draw the bow to see if making things easier helps. If that helps even with the longrod fitted, you can wind it up slowly and try to draw with the same amount of smoothness. Once you feel it, it can be easier to get it right with your normal draw weight.