I have a modem over a phone line. Why can't it ever connect at more than 56 kbps?
Modems are designed to work over the classic phone network, which only ever supported 8kHz samples of 8-bits each. This provides an absolute maximum of 64,000 bits per second.
In order to support actual modem speeds higher then 33.6 (aka 56kflex, x2, v.90/v.92), one end of the connection must be digital, and there can only be a single analog to digital conversion in the communication path.
Given that most consumers have a modem connected to a standard POTS line, this is the first and only analog part of the link. On the service provider's end, there is a PRI, BRI, or channelized T1 providing the digital side of the link.
DSL tech, even though it runs over the same copper, uses very different technology in frequencies outside the normal voice ranges, and thus can obtain higher performance then plain old modems.
Because modems have to operate within a certain set of frequencies to be properly supported over analog POTS lines, this is part of what creates the 56kbit ceiling. The FCC, due to power and signal issues, further limits the connection to 53kbit.
The FCC only allows a modem to connect at 53.3k. Even if the modem itself reports 56 or 54 or something higher than 53.3, it won't be higher than that in actuality. Additionally, most often the connect speed you see, if it is accurate, is only the initial speed, actual average speed can often also be lower throughout the duration of the connection due to line quality, connection quality, etc etc.
So really in the end it isn't so much a limitation of the technology itself, but of the FCC and the quality of the carrier.