During reboot the serial controller is reset. This drops the modem control line Data Terminal Ready. This in turn instructs the modem to hang up.
Avoid the temptation to configure the modem to ignore DTR. This leads to a worse bug, where the telephone line does not clear down correctly, the modem is engaged, and there is no way to clear it. Ignoring DTR also gives no way to clear hostile callers from the line.
You may wish to record the amount of time that the computer takes from Restarting system to the boot loader prompt.
The modem may also hang up during the boot process (as the serial chip is reset) or when the init run level is changed (as getty is restarted).