The most common reason for restricting the time range of the data analysis is to exclude times when the background count rate was abnormally high due to variations in solar activity, or due to changes in the local space environment as the spacecraft orbits the earth. If the light curve shows periods of significantly higher count rates, excluding those times may improve the quality of the subsequent analysis. If in doubt, it may be useful to perform the same analysis with and without excluding the higher rate intervals to see if it significantly affects the derived results.
Note that most long observations from space observatories in low earth orbit are broken up into many discrete observing intervals due to earth occultations and other operational constraints. These basic 'good time intervals' are already defined in the 'GTI' file that is associated with the observational data, so you usually do not need to carefully select the start and stop of each of these instrumental time periods. Any time intervals that you select will be combined (ANDed) with the basic GTIs.
If the flux from the astronomical source(s) in the field of view might be intrinsically variable, then care must be taken to distinguish instrumental background variations from actual changes in the flux from the sources themselves. In this case you may need to compare the flux from different spatial regions of the detector to determine if the flux variations are due to global background variations or are localized to certain sources. Note that if the flux has been integrated over the entire area of the detector, then small flux variations in individual sources may have a negligable affect on the overall light curve.
When studying variable sources, it is sometimes desireable to select times when the sources is in a particular state, for example, during a bright outburst or a faint eclipse. For maximum sensitivity in this case, one should plot only the flux from the source, excluding as much background as possible.