What cell type? If you are using a mammalian cell line, there are many things that you'll need to consider. Temperature, humidity, pH, and media volume are probably the main ones though. Most mammalian cells are cultured at 37oC. If you let the cells get too cool, some of their metabolic processes may cease resulting in cell death (or detachment for adhesive cells). If the head space over your media is not humid enough, concentrations of media components will increase as the water evaporates from the media (salts will be most problematic). If you are using standard cell culture media then you need to provide CO2 in order to maintain the media's pH buffering capacity. The cells will be acidifying the media so the media must either have a large volume, provide some buffering, or be replaced frequently to prevent acidification from killing the cells. Photo toxicity may certainly be a problem but maintaining the correct culture environment will allow the cells to repair some damage between exposures.  We have done a number of 72 hour and longer fluorescence studies where we are taking 4 images every 30 minutes (1 DIC and 3 fluorophores) and we are able to maintain healthy cells for the duration of the experiments. We often introduce toxins and then watch how the cells to recover.

I am assuming the fluorescence isn't killing them? Many GFP/RFP fluorescent tags are poisonous at high concentrations and tagging cells with chemicals or antibodies also can kill cells very easily. So presuming it is not the above issues, the actual exposure is also a problem. If you use halide or mercury the heat/uv/light excitation will kill cells even at 300ms, especially closer to the UV wavelength. One option is to use fluorescence closer to far red (ie Cy5, APC, etc) the damage to the cells will be much less. Another option is to use LED excitation for your fluorescence, which will also minimize damage to the cells. 

What cell type? If you are using a mammalian cell line, there are many things that you'll need to consider. Temperature, humidity, pH, and media volume are probably the main ones though. Most mammalian cells are cultured at 37oC. If you let the cells get too cool, some of their metabolic processes may cease resulting in cell death (or detachment for adhesive cells). If the head space over your media is not humid enough, concentrations of media components will increase as the water evaporates from the media (salts will be most problematic). If you are using standard cell culture media then you need to provide CO2 in order to maintain the media's pH buffering capacity. The cells will be acidifying the media so the media must either have a large volume, provide some buffering, or be replaced frequently to prevent acidification from killing the cells. Photo toxicity may certainly be a problem but maintaining the correct culture environment will allow the cells to repair some damage between exposures.  We have done a number of 72 hour and longer fluorescence studies where we are taking 4 images every 30 minutes (1 DIC and 3 fluorophores) and we are able to maintain healthy cells for the duration of the experiments. We often introduce toxins and then watch how the cells to recover.

If you can't use CO2 to provide a proper pH to the culture media using 25-50mM HEPES will help.  This is only one of the big issues.  The other is phototoxicity as Ron mentioned.  The exposure time or frequency is not necessarily your issue, but how much light.  Full exposure to widefield epifluorescence can generate a ton of free radicals that reduce cell viability.  We use Oxyfluor from Oxyrase to reduce free radicals.  It acts as an oxygen scavenger. Add it to your medium just before imaging at a 1:100 dilution (spin it down first: it is "chunky"). Attached is a great commentary on live cell imaging that I have given to many researchers starting to do live-cell fluorescence microscopy. Good luck.

Incubation with CO2 infused humidified air, refreshment of imaging buffer by drainage and perfusion, low laser power and imaging only at minimally required intervals. Using equipment like Definite Focus on ZEISS microscopes helps in finding back focus with varying factors induced by long term imaging.