I have a significant other living abroad and I want to visit them every 3 or 4 months. Currently, I am a permanent resident. Is it okay if I travel abroad every 3 or 4 months and stay outside of the US for about 1 week each time?
Yes, that's totally fine.
Unfortunately US immigration officers have a lot of leeway and the exact rules are somewhat vague, so it's possible that you might get questioned about it. However, that's unlikely since 1 week per quarter is very far away from anything that could be considered as abandonment and is much less than many regular business travelers do.
I highly recommend applying for Global Entry (if you are eligible). It greatly improves accelerates the security (comes with TSA PreCheck) and immigration experience and has saved me many connections.