either he is staying in Marlinspike for a really extended period of time(apparently for no reason) or he has moved his lodgings to Marlinspike
I think that most of this reiterates points raised elsewhere, none of which actually provides an answer or evidence that is conclusive.
For example, I think that if Marlinspike/ Moulinsart is in the same relation to Brussels as its real-life model of Sart-Moulin, then it is but a short train-ride or bus journey from the city.
Hergé knew Sart-Moulin because of trips made with his father, when he went to visit his boss at the country house he used in the summer to give him updates on the business he owned. The boss had a place in Brussels too.
Likewise, Hergé's beloved place at Céroux-Mousty provided a tranquil repose away from his home in the city, but it wasn't a replacement, it was an alternative away from the hustle and bustle.
Tintin may have spent long periods at Marlinspike, and may have even arranged for Mrs Finch or his office to forward mail, without ever actually
moving there. People (other than Chang, who as MCT16 points out, was out of touch) may have known where to reach him at different times of the year. I mean, Tintin was holding down a job at the magazine that bore his name during these years - it would seem convenient for him to have a pied-à-terre
so that he didn't have to slog back to the country after a late night editing... ;-)
I think that MCT16's point that Tintin might feel that the Captain was lonely would also be a good reason to visit for extended period, but as both Tintin and Haddock do do things separately (Picaros
springs to mind), showing that they can manage independent living, I don't see that as evidence for where he lived permanently.