Well, it depends a lot on the cause- I know the sources for my own pain issues, so I can kind of go off of there, but in theory any sort of complex moving body has the risk of chronic pain, be it organic or cyber.
One of my major issues with pain is related to mobility- this runs in the family, stiff joints and muscle strain, a lack of cushion between bones or improper development of said bones. For cybertronians, replacing joints or whatever’s needed to lubricate them might be easier than it is for humans, but if their body can’t manage to upkeep of these joints I imagine any sort of mobility-based pain would return quickly. In most of my setting Cybertronian bodies function more or less like organic ones, with nanites and specific systems dedicated to various bodily functions, and sometimes there are inherent flaws that result in continued failure of these functions. Sometimes they can be treated, but other times there’s something perhaps spark-deep or the result of traumatic injury that refuses to let the body heal.
My other pain issues start at what is effectively the source of all pain- the brain and nervous system. Phantom pain and I are well acquainted friends, usually triggered by fatigue or other stressors, and it’s hard to recognize when there’s pain because something in your body is actually hurt, or because your nervous system is basically so stressed it’s crying. This might be a major issue for Cybertronians because pain that exists in the processor or spark may be similarly difficult to identify and treat without extensive and continual care- for me, antidepressants help, and they help a lot, but this also comes with the reality that if those fail- pain is waiting to return.
So that’s two options- cybertronians are full of moving parts and when those fail to work in tandem, chronic pain could result, or otherwise pain can stem from something deeper and less physical.
As for other options…chronic pain could be the result of illness or chronic illness– maybe a rust disease causing degredation internally, even if the immune system can repair and keep things going it would still be unpleasant or painful and certainly tiring, the constant repairs/re-repairs so on so forth. Or even a parasitic attachment, scraplets as the equivalent of tapeworms, just waiting in deep systems, passively sucking away life.
An old injury that never healed fully and instead other structures healed around it.
An unidentified allergic reaction or intolerance to an impurity in energon or paint (I mean, can you imagine cybertronian lactose intolerance?)
Stress from a million years of fear and warfare, when abated, suddenly the body doesn’t know how to handle not being constantly ready to fight, to die, and the pain starts because the brain is trying to find an outlet because something must be wrong, something.
So on, so forth! I think it’s an interesting avenue to explore, the causes and treatments of chronic pain in cybertronians.