A 28.8K connection on some real-world lines may not occur very often, if it occurs at all. Both the originating and the answering modem are adjusting to their line conditions during the connect phase. The easiest way to find out if its your phone line or your modem is to find someone who usually gets 26.6 or 28.8 connects, and try your modem on her system, or his modem on your system. You will most likely find that the problem at your end is phone-line related. The part of the telephone system which you may be most able to improve is your telephone premises wiring.
Some modems work better cold than hot, and vice versa.
Generally speaking it is a good idea to make sure that the modem does not get too hot. If you have your modem connected to the phone line through a surge suppresser, try it without the surge suppresser. Many surge suppressers can interfere with modem communications. If that doesn't help, listen carefully to the quality of your voice connections. Note that you must dial a known quiet number, since many otherwise good phone lines exhibit excessive noise until you actually connect.