Landlord Responsibilities on Repair

[Erwin U.]

Hello, Frequent visitor to this forum to learn about landlord for the last few years and have a few rental properties in DFW area. However, this time I need some feedback from other landlord. I understand that landlord is responsible to repair anything that related to health, safety and habitability of the tenant and the property. 
There is an existing long term tenant with one of the property that I acquired last year.  However, in the past few months tenant have comes up with lists of repairs and request. 
I have made most of repair/replacement such as: install new toilet flapper at multiple toilets, repair stuck window blind that never been fixed since she moved in, replace multiple Closets door ball catch that stuck, blocked Dishwasher air gap valve due to build up dirt from dishwasher. But I refused to install water filter to the refrigerator that doesn’t equipped with filter and was provided “as is” for tenant to use by previous landlord/owner per lease. 
This weekend tenant ask me about shower rod in one of the bathroom  that fell down to be repaired, but I declined the request because I never provide/supply shower rod with other tenant/properties. However, I don’t know the history about this particular shower rod. 
Tenant were upset with my respond and ask me what is my responsibility to provide/repair as landlord. Tenant argument is they have to provide and repair everything. 
Fellow landlord, do you have any suggestion or feedback? Thank you in advance.