So the technician changed my modem to an Actiontec GT784WN. I now have access to the transceiver statistics.
I've already had like 20 disconnections today and my speed -which can go up to 10000 kbps in the morning- dropped to 2000-4000 kbps. So I'm copy/pasting my stats here in case somebody can pinpoint a problem somewhere.
Connection : Status
| Broadband: | CONNECTED |
| Internet Service Provider: | CONNECTED |
PPP Parameter : Status
| User Name: | N/A |
| PPP Type: | PPPoE |
| LCP State: | DOWN |
| IPCP State: | DOWN |
| Authentication Failures: | 0 |
| Session Time: | 0 Days, 00H:00M:00S |
| Packets Sent: | N/A |
| Packets Received: | N/A |
Broadband Parameter : Status
| VPI: | 0 |
| VCI: | 35 |
| Broadband Mode Setting: | ADSL2+ |
| Broadband Negotiated Mode: | ADSL2+ |
| Connection Status: | CONNECTED |
| Downstream Speed: | 4387 Kbps |
| Upstream Speed: | 956 Kbps |
| Retrains: | 6 |
| Retrain Timer: | 0 Days, 0H:0M:28S |
| ATM QoS class: | UBR |
| Near End CRC Errors Interleave: | 4061 |
| Near End CRC Errors Fastpath : | N/A |
| Far End CRC Errors Interleave : | 91 |
| Far End CRC Errors Fastpath : | N/A |
| 30 Minute Near End CRC Interleave : | 375 |
| 30 Minute Near End CRC Fastpath : | N/A |
| 30 Minute Far End CRC Interleave : | 0 |
| 30 Minute Far End CRC Fastpath : | N/A |
| Near End RS FEC Interleave : | 0 |
| Near End RS FEC Fastpath : | N/A |
| Far End RS FEC Interleave : | 0 |
| Far End RS FEC Fastpath : | N/A |
| 30 Minute Near End FEC Interleave : | 1998 |
| 30 Minute Near End FEC Fastpath : | N/A |
| 30 Minute Far End FEC Interleave : | 0 |
| 30 Minute Far End FEC Fastpath : | N/A |
| 30 Minute Discarded Packets Downstream : | 0 |
| 30 Minute Discarded Packets Upstream : | 0 |
| SNR Downstream : | 5 dB |
| SNR Upstream : | 9 dB |
| Attenuation Downstream : | 47 dB |
| Attenuation Upstream : | 26 dB |
| Power Downstream | 19.5 dBm |
| Power Upstream | 12.3 dBm |