I think the "have" can be deleted without harming the meanign. Your opinion about the editing?

No it would be better if you took it out and said it like this...

The reproductive organs will get old and may not function properly...But it can always get a tumor even though it may not function properly...

Or...But it can always be susceptible to illnesses, even if it does not function properly...The organs may even form tumors, because it stops working properly...

"Have function" = "Work properly"...And sounds more natural...

The reproductive organs may get too old to work properly....But it can always form a tumor...Or tumors...Because them not working properly, may be why it may form a tumor, or tumors...or any other illness...

And you can even just say "function properly" instead of "have function"...

Thanks