Unfortunatly this is a problem for PRI and it's not the provider or the system. This is what I learned some time ago. It is a cut and paste that makes all this modem stuff very clear.

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You have a T1 into you PBX, voice calls are not a problem, but you can’t send a FAX. The PRI that you are leasing from the LEC is terminated into a Digital Crossconnect System (DSC) at the CO. The LEC uses the DSC to connect the T1 channels to CO carrier channel banks with FXO channel units. This takes the digital channels to analog to connect to the CO switch ports (POTS).
T1 coding has two options ESF/SF (SF is listed as D4 on some test sets) B8ZS/AMI. If the ESF/SF options at each end of a T1 do not match the system will not sync up and the T1 will not work at all. T1 transmission requires at lease a 17% ones density to keep sync. G.711 coding of voice is rich in ones. Data can have a high number of zeros causing a carrier system to have a low ones density. To overcome this B8ZS was introduced. Any time a channel has all zeros; Binary 8 Zero Substitution (B8ZS) will replace the channel with 4 bits with 2 bipolar violations. When the equipment at the other end of the T1 detects the B8ZS code the equipment will replace the four one bits with all zeros.
B8ZS/AMI option must match at both ends of the CO DCS to carrier channel bank. When the DCS is optioned B8ZS and the channel bank is optioned AMI, voice will work ok but Fax’s will fail. This is difficult for the CO to find. If your PBX lines are spit between banks and only one is optioned wrong, sometimes you can send a FX sometimes you can’t, depending on witch co line you uses
Just replace T1 with PRI and understand the you are effectively doing this. 56k analog > 64k digital > between 14K and 56K analog. This could repeat itself depending on the total of hops it makes. The modem thinks it's shaking hands at 56K but in reality the remote end is more like 48K. So no handshake no talkie. Noisycow has a valid point, force the handshake to be low and it should be ok.

Hope that helps or atleast makes it as clear as mud. smile