A couple of rules of thumb come to mind from tuning loops over the last 40 years for the chemical process industry on how you might want to reset the reset time.
The Lambda tuning rule reveals the nature of the problem people get into for loops with vastly different speeds of response. Per Lambda tuning the reset time should be set equal to the largest open loop time constant in the loop for self-regulating processes. For fast loops, the time constant is on the order of a few seconds. For many important slow processes in the chemical industry, the time constant can be thousands of seconds (2 to 3 orders of magnitude larger).
For fast loops such as liquid flow and pressure and inline composition control, I found the reset time was usually too high (repeats per sec too small) and the controller gain was too large (proportional band too small). The result was a hesitation in the approach to set point. The largest time constant is normally not in the actual process response but in the sensor, transmitter, valve, and DCS filters. Consequently the reset time in fast loops depends more upon the dynamics of the automation system. From another perspective, more reset than gain action is desirable for fast loops to smooth out the likely presence of noise due to a lack of an appreciable time constant in the process itself.
For slow loops such as vessel pH and reactor or column temperature and pressure control and integrating loops such as level and batch composition control, I found the reset time was usually too low (repeats per sec too large) and the controller gain was too low (proportional band too large). The result was an overshoot in the set point. For integrating loops, you can also get slow rolling oscillations from the double whammy of too low a reset time and too low of a controller gain (see TNT on Level). For runaway reactors, the combo can be downright dangerous (see TNT on Runways). From another perspective, more gain than reset action is beneficial to provide preemptive action that is cognizant of the direction of the change in error.
Even though I was keenly aware of these rules of thumb, I was embarrassed one time by my colleague when he suggested the plant first increase the reset time by a factor of ten or more on a pH loop before they go to the trouble of implementing an advanced control technique in a PLC (not a pleasant experience). The increase in reset time improved the loop response so much that the linear reagent demand control technique I proposed was not needed. This was a hard reminder that you should always tune the loop before advocating more sophisticated controls.
If a loop is not keeping up with a load disturbance, you need to increase the reset action. However, this can be achieved by an increase in the controller gain rather than a decrease in the reset since the reset mode is the result of both tuning settings (e.g. reset action is proportional to the controller gain divided by the reset time). This is particularly important for integrating loops where the product of the controller gain and reset time should not go below a low limit that is 4 divided by the integrating process gain to prevent slow rolling oscillations. In other words, unless you are sure you are at or above this limit, you should preferentially increase the controller gain for integrating process to increase reset action. If there is noise or a stepped response from an analyzer, the measurement filter should be increased to prevent an overzealous kick from proportional action and a feedforward signal be actively pursued to help deal with the shifting load.
For integrating loops, the Lambda tuning rule sets the reset time equal to twice Lambda (closed loop arrest time) plus the loop dead time. This rule maintains the product of the controller gain and reset time at the optimum low limit. Assuming you know the integrating process gain, load rejection is optimally increased by decreasing Lambda, which simultaneously increases the controller gain and decreases the reset time.