To me it suggests an unwillingness to allow the moment to pass, to gracefully exit. Seeing a house still covered in fairy lights mid January, or watching a christmas tree slowly wilt in the mid summer sun, day after day, is kinda like staying until the very end of a party: you do it because you want to have more fun, but it ends up being really lame and boring.
To me it highlights the logistics of Christmas (which are so often the source of argument). You can imagine someone repeatedly asking their frazzled partner to, for gods sake, take down the fucking fairy lights, it's mid February! And the frazzled partner putting it off because it's such a fucking nightmare taking it down and, besides, the lights never go back into the box neatly anyway, so why not just put it off a few days more. And anyway, it lights up the neighbourhood.
And so it continues and Christmas just becomes a time where you DO STUFF THAT YOU DONT REALLY WANT TO DO and then it ends and you are relieved, but there are things you need to do, like throw the Christmas tree out, and take down the fairy lights. Not to mention eat ham for the next three weeks straight to get rid of the ham we have, which we didn't really want, but somehow felt compelled to buy.
Somehow, christmas things post christmas, represents decay, stagnation: evidence that there is an unwillingness to move forward, to change. Doubtless this phenomena exists at all times of the year but, with christmas decorations, it represents tangible, physical proof.
Just like a broken window that stays broken tells us something about the circumstances of the person who lives there, we can conclude various things about people who leave out Christmas lights well past Christmas.
And, rightly or wrongly, it makes me a bit sad.