There are still some options you can try.
FIRST thing, WHAT TYPE of service is this? Is this Cable internet, DSL, FIOS, what? I am not familiar with FIOS service, so I will give you suggestions for cable or DSL connections. Depending on the type of modem you have, you SHOULD be able to connect to it, and see some kind of diagnostic page which will show you line statistics.
If you have DSL, take your modem out to the back of your house (possibly inside, depends), to the NID (Network Interface Device). This is typically a gray box where the telephone wires come into one end from the pole, and the other end goes into the house. Unless you have some kind of a 'line service' with the carrier, anything on the INSIDE of your house is NOT the ISP's responsibility. There should be a phone jack inside of there, and that is the Demarcation point. If you have a telephone line with it as well, you can plug the phone into that, and get dialtone. WELL, UNPLUG that, and plug your DSL modem in right there. If you STILL have the trouble there with a known good cable, and a good modem, then the trouble is from the telephone company, and you need to get them out to fix it. Emphasize when the trouble occurs, and that you want a tech to be dispatched at that time.
I would show you a pic of the NID at my house, but I am at work, and it will be dark by the time I get home. Here is one I found on DSL reports that is an animated .gif that shows it both opened and closed.
If you have cable, the same type of thing applies. While the cable company doesn't really have a NID or demarcation point per say (at least not at my house, my yard has a pedistal in the back corner of my backyard, and a burried cable that comes up and enters the house at the same spot that the phone line comes in) you might be able to do this from inside, might not. I know at my house that there USED to be a splitter on the OUTSIDE of the house that brought the cable inside, and around the house from the exterior, but I ripped that junk out, and recabled the house (almost done). Locate the first in-line connector that you can, and connect up the cable modem. If the problem persists from there, again, call up the ISP, have them come out.
I would have to ASSUME the same would be true of a FIOS type fiber service, but I don't have it, haven't ever seen an installation of it, so I don't know if it is fiber INTO the house, or if it is a fiber to copper handoff in the NID at the back of the house (guessing that there would be a NID).
JUST A NOTE.... If you perform either test that I suggested above, ALL of your services connected to that line from the carrier will NOT WORK if you are testing it.... IE: NO PHONE, NO INTERNET, NO TV (assuming they all come through the same connection). You will have connectivity from where you are connected, but the whole house will be "dark"... Just want to warn you, had some friends try those steps, and got chewed because they didn't realize that would happen, and I didn't mention it because, DUH, figured it was kind of obvious.
As long as you are absolutly 110% sure it isn't something in your home which might be envirmental as Harper suggested, or sunlight issues as anohteruser suggested (I have seen this documented a few times in the past 7 years) with work, there is another option. Given the duration, I would lean towards something thermal, sun rises, hits component x, heats it, metal expands, connection is fine, sun sets, metal cools, contracts, loss of signal. Typically, I would assume this would go DOWN COMPLETELY the whole time, but I suppose it is possible to have a large number of errors on the line due to that.
Your ISP might tell you that it would be billable, but talk with them to see if you can have a tech dispatched out to your premise when the trouble occurs, and have them use some kind of diagnostic device to see if the trouble is coming from the LINE, or your HOME. As I said, I don't know if an ISP would do this, and they might charge for it.
Like was mentioned earlier, chat it up with neighbors, and see if they are seeing the same kind of thing. Share DETAILS. You neighbors might not see the issue because they are in bed watching Matlock at 7:30pm, 30 minutes before the issue starts.... hahaha. Couldn't resist.
