There are a number of reasons why the tool holder could be sticking

1-The tool holder is pitted, rusted, or has a build up of gunk on it. Using scotch brite is a good way to clean it. Onsrud makes a Cleaning Solvent & Rust Protector which is $25.70 NOTE: If the tool holder is in bad shape and is aged it is recommended to change them Collets, collet nut, and tool holders are consumables. 

2-If the pull stud if over a two years old, I would recommend changing them. This is simply good house keeping. our p/n is: H24G10-ISO30PS3 - $28.50 each (assuming you have HSD 5HP ATC)

3-If you are cutting aggressively, the spindle could be heating up thus expanding the metal tool holder causing the sticking. If this is the case I'd recommend adding a cold air gun to apply cold air to the tool holder as it cuts. 

4-Spindle nose cone. If there is a build up of gunk and dust in the spindle nose cone this could be causing the problem. The spindle is sealed in all areas, accept this section.  Over time dust and debris could have entered the spindle causing problems. I would recommend carefully cleaning inside the spindle nose cone. Do not blow air up into the cone. This will force dust and debris to enter further into the spindle body. If you see allot of build up, it may be better to send the spindle to HSD for rebuild, before something catastrophic happens.