Thanks for everyone's input.
The main issue was Louie's point, the ADXL345 is a QFN part and I had a bad solder joint.
From the ADXL345 data sheet, the read/write addresses are given as $A6 and $A7 which do take into account the read/write bit and it is this value used in the I2C PBP code. I added a label to the I2C commands which allows a jump if there is an I2C communication error talking to the device. I added this label for all commands sent whether read or write, this error occurred for every command which directed me to investigating the hardware. Adding the label was a very valuable diagnostic tool.

Below is my working code for the ADXL345, much more work is still needed to get the device configured for my application and get the raw counts into meaningful values. Overall the PBP I2C commands work great and are simple to use.

Code:
X0 var byte
X1 var byte
Y0 var byte
Y1 var byte
Z0 var byte
Z1 var byte
ID       var byte
Mode     var byte

high ADXL345_CS ' Set high to put unit into I2C mode
pause 1         ' Added to insure no R/W issue
low ADXL345_SDO ' Set low to put unit addresses to $A6, $A7
pause 1         ' Added to insure no R/W issue

serout2 RS232_TX, 6, [13,13,10,"Start of Test Program. "]

'Initialize ADXL345
I2Cread ADXL345_SDA,ADXL345_SCL, $A7,$00, [ID], I2C_error 'read Device ID
serout2 RS232_TX, 6, ["Device ID: $", hex2 ID,13,10]   ' Value should be $E5

I2CWRITE ADXL345_SDA,ADXL345_SCL, $A6, $31, [$0B], I2C_error  '+/-16g, 13-bit mode
pauseus 5
I2CWRITE ADXL345_SDA,ADXL345_SCL, $A6, $2D, [$08], I2C_error  'Start Measurement or put into Run Mode
pauseus 5

I2Cread ADXL345_SDA,ADXL345_SCL, $A7, $2D, [Mode],I2C_error  ' Confirm mode setting
serout2 RS232_TX, 6, ["Mode: ",hex Mode,13,10]     ' value should be 8
pauseus 5

Main_I2C:  ' Main Loop
   I2Cread ADXL345_SDA,ADXL345_SCL, $A7, $32, [X0,X1,Y0,Y1,Z0,Z1], I2C_error
   serout2 RS232_TX, 6, ["X,Y,Z, ", Sdec 256*X1+X0,", ",Sdec 256*Y1+Y0,", ",Sdec 256*Z1+Z0,13,10]
   pause 100
Goto Main_I2C

I2C_Error:
    serout2 RS232_TX, 6, ["I2C Comm Error",13,10]
stop