Thanks for the responses
.com and
rufusdrumknott. I figured it out: connection issue between the 3DS and my router, apparently. Reset the router and it worked no problem. Funny thing is, my laptop never lost connection, but then I would assume my laptop has a stronger antenna.
So, my follow-up question (and yes, I'm googling as I ask, I just wanted to know if anyone here more connected to the technical side can help me find an answer faster) is if 3DS XL models have documented problems with the wifi antenna / card wearing out or losing sensitivity over time? Because that was annoying, and this is the second time this has happened. That is, the second time I've unexpectedly lost the ability to access the internet on my 3DS (the last time was yesterday; though I just stopped playing and went to bed that time).