One of the primary mustahab things for a deceased body is that it is quickly washed, shrouded and buried. There are numerous ahadith from Ahlul Bayt (a.s.) that point to the hastening in the process of laying the mayyit to rest in his/her grave.
As for burying the body quickly, besides the health reasons, the family of the deceased also need to vent their emotions and have a fixed place where they are able to mourn and then regularly visit.
However, if there are valid reasons for postponing the burial, then there would be no problem in that.
And Allah knows best.