อยู่มานาน mean lived for a long time, stay for a long time
อยู่ = live,stay
มา = come
นาน = long time
มานาน in this case, it's telling that you do something for a long period of time.
ex. I live here for a long time.
I stay here for a long time.
I'm in the same position for a long time but don't get a promotion.
รอ/มานาน = wait for a long time
หา/มานาน = find for a long time
ทำงาน/มานาน = work for a long time
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Note: If you add "ตั้ง" like มาตั้งนาน it's make the sentence more "bold", use with friends.
When your friends is late and you wait them for an 2 hours and you get a bit upset.
So when them come you say "ฉันรอพวกเธอมาตั้งนาน" = I've waited you guys for so long.