The entire problem here is the division of "us" and "them". From the customer's perspective, you are both "them". If the product doesn't work, you're both to blame no matter whose fault it was.
Work with your developers to make the application more supportable. Show them the problems you are having and ask for their help in fixing them. Too many sysadmins just throw it over the fence and say "not my problem, you fix it" and that's honestly not acceptable.
This is the entire reason "DevOps" is a thing. They are not fundamentally different roles; you're both involved in building a system that does things for customers. You bring different skills to the table, but that's often the case with every developer: you probably have a dev who is a whiz with databases, another who knows some other library really well... a sysadmin skill set is no different.
"Us and Them" makes it sounds adversarial, but it's not meant to be. It's about who is best equipped to fix the problem. More often than not, a problem with an in-house developed piece of code will be best fixed by the person who wrote that code.
Work with your developers to make the application more supportable. Show them the problems you are having and ask for their help in fixing them. Too many sysadmins just throw it over the fence and say "not my problem, you fix it" and that's honestly not acceptable.
This is the entire reason "DevOps" is a thing. They are not fundamentally different roles; you're both involved in building a system that does things for customers. You bring different skills to the table, but that's often the case with every developer: you probably have a dev who is a whiz with databases, another who knows some other library really well... a sysadmin skill set is no different.