Well, Rivals take your region score down a specific amount, depending on rival type, class and level.
E.g lvl1 FNIX tank will reduce your region score more than lvl 1 mil tank. And lvl1 proto hunter reduces your region score even less.
Also, do note that you don’t need much region score to gain first 10 region levels, only about 2000 score.
Region level vs region score, what i’ve noted so far:
So, when you’d loose e.g 2000 region score after killing a Rival, it depends on what level your region was.
If it was at level 21, with about 12000 score, you’d only loose 1 level, down to level 20 and 10000 score. But if it was at level 9, with 1720 score, it will drop down to 0 region level and 0 score.