Concussion rate and severity are associated with previous concussions.
From a study of college (American) football players:
Players reporting a history of 3 or more previous concussions were 3.0 (95% confidence interval, 1.6-5.6) times more likely to have an incident concussion than players with no concussion history
Slowed recovery was associated with a history of multiple previous concussions (30.0% of those with ≥3 previous concussions had symptoms lasting >1 week compared with 14.6% of those with 1 previous concussion)
Guskiewicz, K. M., McCrea, M., Marshall, S. W., Cantu, R. C., Randolph, C., Barr, W., ... & Kelly, J. P. (2003). Cumulative effects associated with recurrent concussion in collegiate football players: the NCAA Concussion Study. Jama, 290(19), 2549-2555.
In a paper reviewing evidence for mechanisms, Greco et al cite the above paper and some others:
Clinical and experimental evidence shows that the magnitude and duration of deficits is dependent on the number and the interval between injuries
Those with multiple concussions showed greater impairment in sustained attention and executive functioning (Wall et al., 2006)
While rTBI does not lead to morphological changes, it can induce structural changes including cortical thinning and enlargement of ventricles (Goddeyne et al., 2015). White matter axonal damage, and β-amyloid plaque formation, has shown to increase following multiple mild brain injuries as well (Prins et al., 2013), (Prins et al., 2010), (Grant et al., 2017) and has been linked to cognitive deficits including executive function and motor speed (Wozniak et al., 2007) and neurodegenerative disease (Grant et al., 2017). Astrocytic accumulation and impairment in a novel object recognition task were also exacerbated following multiple injuries (Prins et al., 2013)
Greco, T., Ferguson, L., Giza, C., & Prins, M. L. (2019). Mechanisms underlying vulnerabilities after repeat mild traumatic brain injuries. Experimental neurology, 317, 206-213.
As far as mechanisms, Greco et al propose "metabolic vulnerability" which is not particularly specific but includes:
following even a mTBI that there is an increase in glucose uptake due to changes in excitatory amino acid release, combined with a dissociation of cerebral metabolism, resulting in metabolic crisis (Giza and Hovda, 2014)
This acute phase lasts 6 h in experimental TBI models and is followed by a period of glucose metabolic depression
They also mention animal studies that seem to provide some causal support this model. However, it's difficult to be certain about causes in humans because there are also likely risk factors experienced by particular individuals due to their age, sex, and genetics/development.
From a neuroscience perspective, yes, this is related to the "calcium entering the nerve cell" mentioned in the linked article, but it's a bit difficult to explain the relevance of this to people who are unfamiliar with neurophysiology. I think it's best to frame this in the context of excitotoxicity, a type of damage to neurons that occurs in a broad range of conditions.