Sounds exactly like my issue, which you can read about here:
»TekSavvy - glorified reseller, not ISP
I'm quite certain the problem is maintenance. I doubt you swapping your modem will get you any benefits ... the issue at the heart of the matter seems to be Rogers is doing maintenance / upgrades, and TSI seems to have no ability to improve the situation. I agree it's ridiculous that this "maintenance" goes on for so long - something is wrong with the way they're going about it.
I currently have a ticket (one of many that they've opened with Rogers) in "escalation" to the network team, but I won't be surprised if it comes back as "no problem found" or the same answer you got, which is that they are doing upgrades in my area. I'm just about done with TSI, to be honest. I don't know that switching back to Rogers will make things better, but I do know that I didn't have these extended headaches with them when I was. Either that'll be the case again (which, to me, makes it worth the slightly higher monthly cost), or I'll just have to find another solution.
FYI, this started late July for me... although it hasn't been daily. I'd say, altogether, in the range of 35+ nightly issues over this period.
If you want a better way to track what's going on, you should set up a Line Monitor:
Won't improve your situation, but it'll tell you exactly when the problem is happening (with a certain degree of precision - I've found that low-level packet loss doesn't always show up).