It should. I keep mine from slipping down with a simple Nite Eyes Gear Tie you can get at tractor supply or whatever I think they're like 8" long. Once I'm at hunting height I just wrap it around once or twice between the delta link and the down line (Your tether) you're attached to so if I enter a little slack in the system by adjusting around my platform or whatever it will stay up there. Then simply uncoil it out of the way before you rappel down but be sure you put your dyna-glyde up there so you can retrieve your rappel line. I've linked a couple of useful videos for this. The other thing is during the later part of the season when the weather is rainy or snowy,, I do what
@boyne bowhunter suggests and use a separate tether so my rappel line is stowed in my pack or a pouch and it will not get wet. Once I'm ready to head out after my hunt, I switch from my tether to my rappel line. I have everything rigged up, both my tether and my rappel line and this is where the other bridge can come in handy too, I then do not have to use a LB to take my tether down and transition to my rappel set up as both are hooked in before I switch my weight over from my hunting tether to my rappel line. You may introduce a bit of slack into your system when making this transition but not much and I just put my rappel line a bit higher than my tether to help with minimizing slack during the transition too. Alternatively, just use your LB as your bridge and then you have the LB there already when setting up your rappel down. A lot of different ways to skin that cat. The first video below from DIY Sportsman speaks of the Nite-Eyes Gear Tye to keep your rappel line from slipping down.