It's not a limitation of the tpic chip. The problem is probably the clock and latch lines. They go in parallel to every chip, and have to go over a much longer distances of wire.
You could try some buffer chips. Many basic 7400 series logic chips can be used, such as 7400, 7404 etc. After the 16th shift register, buffer the clock & latch lines. Same after the 32nd shift register. The data line should be ok because that gets buffered by each shift register.
Additional Note (suggested by Paul_S): "7400" logic series were invented back in the 1960's. Since then, newer replacements have been developed using newer technologies. The chips we buy today are usually the "LS" or "HC" versions, so for example the 74LS00 or the 74HC04. Either will be fine for your circuit. Buy whatever's cheaper.
Also, you must have a 1.0uF bypass cap for each chip, near the 5V & ground pins. Depending on what the chips are driving, and how fast switching is happening, lots of smoothing caps is also a good idea.
Something to test: could the 24th or 25th tpic chip be faulty? Try swapping some chips around.