Because he is logging in, even if its for 5 minutes their not going to agree with you that he is inactive. There is a generic answer for this in the help section which is basically what another poster stated. When the guild leader is inactive for a period of time (I read 8 weeks) the system automatically looks for the longest active member and gives them the guild leader role.
So with what you said. (Don't take this the wrong way) Put yourself in another guild members shoes and ask. What makes you think you should be the guild leader. Just because you log in more time in a day doesn't make someone else a bad leader. And there in lies a problem with BioWare getting a ticket. Just because you want to be the guild leader, doesn't mean others dont and it wouldn't be fair for BioWare to side with anyone. So it would put BioWare in a predicament.
I might suggest you get together with a group of friends and send mail to the current guild leader with your concerns and see if they are willing to give it up, or explain their inactive status. If not, then you may want to take a group of people and go start your own guild.
Uhm, they think they should be the replacement GM because they are the co-owner of the guild? An in game mail is a good idea though.
OP, it's not the person that spends the most time online, it's the person with the most seniority. If you co-own the guild then I'm guessing you and the GM started the guild together and that gives you seniority over the other members, since you were there before everyone else. If you are a relatively new co-owner however, the first active person that the GM subbed into the group would get the GM title if he stays gone more than 30 days. I believe it's been changed from the 60 days mentioned in the original faq.