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Chilled water coil won't condensate
If the chilled water temperature is "scheduled", or reset based on OAT, and it runs at a higher CHW supply temp than originally designed, then the coil may not get cold enough to create condensation.
With an entering air condition (assumed from your post) of 73%RH at 72F, according to the psych chart, you need an average minimum CHW temperature in the coil, and corresponding leaving air temperature of at least 60F to start condensing moisture from that airstream.
If in fact, your CHW entering temps are the usual 44F, to a leaving temp of 56F, you should be condensing like mad. If you are not, then yes, you could have too high an air velocity through the coil and you aren't cooling the air off enough to condense much. Information is required as to what is the entering and leaving air conditions at the coil as well as the average face velocity - should be less than 500 feet per minute depending on coil configuration (4-row, 6 row, how many fins per inch, etc.)
The other part of the issue is if the CHW control valve is modulating only based on space temperature, you may need to run the cooling coil and control valve open more often based on space humidity to accomplish the dehumidifcation function, and then reheat the supply air to maintain space temperature. This is a common Museum/Archives/Art Gallery design- the cooling coil has to be designed and controlled for both space temperature as well as dehumidification, and many time you need reheat after the cooling coil, as the air gets cooled off too much by the dehumidification function.