I think this is a poor question because there is little to choose between continual and continuous. They are both adjectives and are considered to be synonyms.
However, even synonyms can be used differently and if I was forced to choose, I would choose continual as the best answer.
To me, continuous more suggests never stopping, within the time period that we are talking about, while continual suggests ongoing/continuing over a period of time but with intervals during which the action stops.
The continuous roaring of the engines made it impossible for us to get much sleep.
Their continual wars during that 100-year period resulted in no gain by either country but much hardship for both.
In your sentence, there are ongoing complaints, day after day, but they are not continuing 24 hours a day.
Having said all that, someone might disagree with my interpretation but ,if so, that would prove the point that the two words are quite similar. Alan hasn’t said which word he prefers, but from what he did say he might also choose continual.