Does you monitor work continuously for a period of time, then start turning on and off? If so, I would try the following which ever is easier in your case then move onto the next one.
_a) Power off you computer for a one or two hours; then turn it on and write down the time it was turn on, and approximate room temperature, and get an approximate time when the screen/display/monitor starts flashing; and the room temperature.
_b) if your monitor has a brightness adjustment turn it down to the lowest level that is tolerable /desirable for you (this should consume less power; i.e., indicates thermal problem), it doesn't need to be at 100% brightness unless lower brightness is not tolerable for your situation. This assume your monitor has such an adjustment.
_c) Reduce the bits used per pixel from True Color (32 bits) to High Color (16 bits) for Window 7
Control Panel > Display > Adjust Resolution > Advanced Settings > Monitor Tab > Color (selection True or High Color). If this is tolerable on quality of display by using High Color go with it; some people see significant difference in the quality of the display, I do not however, no difference.
_d) Pull or reposition the monitor so that it is a couple feet away from the wall, and if available point a room fan into that space or back of monitor, after it has been turn off for one hour for good air flow.
_e) Perhaps turn down your Air Conditioning and try early in the morning and have the monitor in an area with good air circulation (perhaps use a room fan or like)
_f) Bring your monitor to a place that has a air compressor (commercial or industrial quality (not the local gas station, probably doesn't have “gadget to remove separates the water” a water separator is what I think it is called… these (commercial/industrial) typically have a water filter/separator to remove water from compressed air line) to blow out dust from the back of your monitor (then try above steps). I doubt a compressed air can for $4.00 at a discount store has the same volume, nor PSI … bring your computer too and laptop if you have one an blow them out also. (test for no water in air jet/stream/flow prior to using it on your computers or electronics)
_g) Most problems with electrical and electronic equipment has been proven to be electrical connectors; check the connectors, you can even try the connectors inside the monitor (see you tube possible disassembly instructions). This might be related to thermal problem, metal expands. Tape is use on several of my connectors in my monitors to secure the connector typically only on the ribbon cable connector. Also try a short and known/proven monitor cable (VGA./DVI/HDMI) a ground pin or other might of open broken (also no sharp right angle turns in the cable)
_h) There might be a electrolytic capacitor that is shorting out, a “dendrite” for instant shorting out an electrolytic capacitor, then the high current burns through the “dendrite” and the monitor “resets”, then it dendrite grows again and causes yet another short
_i) Thermal safety circuitry in the monitor; after a certain temperature is reached the monitor automatically cuts off power (i.e., the monitor “flashes”)
If it not a high end monitor perhaps consider another monitor; If it is a high end monitor, and it is a thermal problem (a monitor that just runs hot), and not a electrolytic capacitor problem, you might consider getting a computer case fan; and a transformer (use a 12 Volt computer chassis fan (Antec) low noise - I would strongly suggest) and place it over the lower air vent (cut out a section of plastic out the back would double air flow, remove the back of the plastic cover from the rest of the monitor before you do this however, would strongly recommend a wire fan guard -see ebay for fan guard) . I had perhaps a similar problem on one of my monitors; two of the same model, one started “flashing/turning on and off” after several hours, There as a 24 Fahrenheit difference in temperature at the upper part of the two different monitors (portrait mode (i.e., monitor sits on it's side not it's “bottom”), which does not help, since the air vents were seemly design for Landscape mode (sits on it's “bottom”) (see step C above, selection here is on/at the adjustment window) , if so, might consider drilling some extra ventilation holes top and bottom (if so remove the back cover prior to drilling holes) Note – Resale value of your monitor by cutting holes in the back, will probably significantly diminish it's value if one ever trys to resell it. Again perhaps you tube web site has a video demo for taking the back cover off.
As a rule of thumb, for every ten degree centigrade the case.die,transistor junction temperature rises, the statistical life of the electronics drop by 50%, geometrical/exponential growth, i.e, a 20 C rise, 25% of it life. If you recap the monitor, make sure one uses 105 C capacitors, not 85 C capacitors, cost probably 5% more in parts cost.
One could use heat sinks on on the back of the interior metal to help on heat dissipation; if you do; I would avoid thermal tape to secure the heat sinks; strongly suggest use only thermal compound (glue/epoxy), it's permanent. Only way to remove the heat sink(s) is by perhaps very high temperature.