I’d recommend looking into getting a breast plate. That will keep the saddle from slipping back down your horses back. As for what kind, as far as I know you can choose to get leather/elastic or all leather. The elastic idea is nice because your horse can still stretch out when jumping, it doesn’t confine him if you know what I mean.
I looked at SmartPak’s breast collars and here’s a nice leather/elastic one….
And here’s an all leather one….
I hope this is of some help, but in other words yes a breast plate would really help you and your horse.
~If you come at it having only 15 minuets it will take all day... If you come at it having all day it will take you 15 minuets~