According to the datasheet you only have a choice of 50mS or 100mS bursts of DTMF data. If your application requires something different, then choose another device.

As for interfacing to the device - what are your connections and code? The phi2 (phase2) signal needs to be high to access the device and may need to change state - note I have not used this device as yet so I'm not talking from experience!

At a guess the sequence to read the device may be:

set R/w hi
set CS low
set RS high or low depending on what register you want
set 02 high
read the 4 bits of data
set 02 low

to write:

set r/w low
set 4 bits of data to output
set RS high or low
set 02 high
nop
set 02 low

be sure to observe the timings specified in the datasheet especially if you're using a fast 8051 variant.