Look up the lore on R2-q5 and RA7 (astromech and protocol droid respectively on the 1st death star)
R2q5 actually stopped ig88 from destroying the death star once; single handedly too.
English
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[i]But do they have the ability to repair themselves and each other? How long before they break down? Especially with no one around to wipe their memories, astromechs tend to become "quirky" over time. [/i]
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Quirky means develop personalities; side effect of their type of ai operating system used. Yea they can fix each other (c3p0 gets put back together by r2) an astromechs are highly adept combat mechanics; imperial protocol droids mostly manage allocation of tasks and designating what resources go where while managing systems per those systems schedules ect. The astro mechs handle the repairs, moving things around with other more basic droids and also network security.