Yes, you can. If you start playing Squad Battles matches early in the week and earn many Battle Points, you might initially be in a top Rank. But if you don’t continue playing matches throughout the rest of the week or earn fewer Battle Points, other players could still be playing and earning Battle Points. That means your Rank could drop if they out-earn you and move up.
On the flip side, you could also move up a Rank if players don’t out-earn you.