Will I keep my Lety-status (LetyBronze/LetySilver/LetyGold) if I withdraw money from my balance?

Yes, sure. When Lety-status is assigned, total amount of cashback earnings is what matters, including withdrawals.

For example, you have cashed out 500 RUB and acquired a LetyBronze status. To receive a LetySilver status, you need to save 2 500 RUB more.