This was a bug in DAQ 7.1, I believe it has since been fixed. But there are some workarounds that will solve the problem for you.
1) Change the value of CI_Max to be less than 214. Due to the bug with the "ticks" units, this value must still be specified to fit the range of the 20MHzTimebase.
2) Just use the "seconds" units and then use the U32 version of read. This will return the ticks value.
As a side note, you may want to consider upgrading to NI-DAQmx 7.2. DAQ 7.2 provides support for digital filters on the 6624. Depending the noise levels of your signals, digital filters may be necessary to ensure proper measurements.
I hope this helps!
gus....