I don't think the science is settled to a degree where we can give a solid answer, or make too many specific conclusions. Disclaimer: I'm not a kickboxer, and I haven't studied the subject deeply.
Getting hit in the head is not good for your brain. Getting hit a lot in the head is very bad for your brain. That's true regardless of dosage, but large, repeated doses of getting hit in the head over long periods of time are particularly problematic.
Medicine has known about the brain damage from boxing and kickboxing for a long time. We have a name for it:
Dementia pugilistica...[is a] variant of chronic traumatic encephalopathy... Symptoms and signs of [dementia pugilistica] develop progressively over a long latent period sometimes amounting to decades, with the average time of onset being about 12 to 16 years after the start of a career in boxing. The condition is thought to affect around 15% to 20% of professional boxers.
I would argue that there are probably a lot of people with minor brain damage that doesn't rise to the level of dementia pugilistica. That damage might be insignificant, but it exists. This is backed up by more recent studies, as reported in the LA Times:
A yearlong study of boxers' and mixed martial-arts fighters' brain activity has found those who fight for more than six years begin to experience damage and those who fight longer than 12 years expose themselves to an even greater decline each time they return to the ring.
The degree of brain damage depends greatly on how you train. Competing seriously is definitely a different animal from training hard, and training hard is different again from training casually. Getting your bell rung is a minor concussion, make no mistake, and those are no good. But in terms of serious damage, I bet a lot of people get a handful of minor concussions spread out over a few years of training and don't suffer any major brain damage. Taking three or four ring fights a year, and the training that requires, would probably mean a greater degree of brain damage. (Not debilitating in every case by any means, but it's certainly present.) Doing this for several years would in most cases cause noticeable problems.
Reading up on the signs of concussions is extremely informative. Staying out of hard training after a serious or moderate concussion is definitely a good idea. It would be a good idea for boxing and kickboxing coaches (in addition to grappling and field sports coaches) to adopt a concussion-recognition protocol. The King-Devick test has been shown to work well for boxing and MMA:
The King-Devick (K-D) test is based on measurement of the speed of rapid number naming (reading aloud single-digit numbers from 3 test cards), and captures impairment of eye movements, attention, language, and other correlates of suboptimal brain function. We investigated the K-D test as a potential rapid sideline screening for concussion in a cohort of boxers and mixed martial arts fighters.
In particular, getting knocked out or losing the match were predictors of damage:
Those with loss of consciousness showed the greatest worsening from prefight to postfight. Worse postfight K-D scores and greater worsening of scores correlated well with postfight MACE scores.
So work on your slipping and defense!
It is also probably a good idea to get regular MRIs or other brain tests done, if you continue to train over several years. As noted in the LA Times article, this is already enforced by boxing commissions.
But in the end, hard training is not knitting class. The risks of learning to hit and get hit can be mitigated through careful control in sparring and diligent use of equipment (and recognizing the limitations thereof), but at some point you're going to get concussed.