If you have landline service, are you hearing noise or static while on the phone, around the time the DSL goes offline?
Step one: Visit http://www.giganews.com/line_info.html and post up the Traceroute the page shows, if you wish. Be aware that your non-bogan public IP Address will show up. It might shown up as the final hop (bottom-most line of the trace) might contain a hop with your IP address in it. Either remove that line or show only the first two octets. What I'm looking for is a line that mentions "ERX" in it's name towards the end. If for some reason the trace does not complete (two lines full of Stars), keep the trace route intact.
For example this what I saw when I was using Verizon
traceroute to 71.242.*.* (71.242.*.*), 30 hops max, 60 byte packets
1 gw1-g-vlan201.dca.giganews.com (220.127.116.11) 13 ms 13 ms 13 ms
2 ash-bb1-link.telia.net (18.104.22.168) 39 ms 7 ms 7 ms
3 TenGigE0-2-0-0.GW1.IAD8.ALTER.NET (22.214.171.124) 4 ms 4 ms GigabitEthernet2-0-0.GW8.IAD8.ALTER.NET (126.96.36.199) 4 ms
4 so-7-1-0-0.PHIL-CORE-RTR1.verizon-gni.net (188.8.131.52) 6 ms 6 ms 6 ms
5 P3-0-0.PHIL-DSL-RTR11.verizon-gni.net (184.108.40.206) 6 ms 6 ms 6 ms
6 static-71-242-*-*.phlapa.east.verizon.net (71.242.*.*) 32 ms 32 ms 33 ms
Step two: Can you provide the Transceiver Statistics from your modem?
#3 If you don't know how to get that info:
a) What is the brand and model of your modem?
b) If you have a RJ-45 WAN port router connected to it: What is the brand and model of the RJ-45 WAN port router?
#4 If you have a RJ-45 WAN port router connected to the modem, even if you know how to get the Transceiver Statistics from the modem: What is the brand and model of the RJ-45 WAN port router?
Temporarilly connect a phone with a DSL filter to the line and check for noise during problem hours. This helps us determine if you need a DSL tech, or if the problem would be faster resolved by a Telephone repair technician. I say this, because it is easier to get Verizon to repair a telephone problem, as landline service is regulated, than it is to get loosely regulated DSL service repaired. When Telephone service is repaired, generally DSL Service follows along.