Dopplers fit into the realm of ultrasound in which high frequency sound waves are used to bounce off sound or images from the baby. Normal ultrasound (not 3D) uses wavelengths approximately 3 times more powerful then just a doppler...
Anyways, the reason it is advised that dopplers not be used everyday or for long durations of time is just to be on the safe side. Using ultrasound or dopplers HAVE NOT been proven to cause harm to humans BUT they HAVE NOT been proven to be entirely safe.
From studies that have been done so far we do know that ultrasound exposure does cause brain abnormalities in rats when they are exposed to it for more then 30 minutes. It heats up the tissues (as it does in humans as well) and in rats after brain dissection it was shown to have prevented the brain cells from migrating to their proper spots which in turn caused brain characteristics associated with autism in humans, abnormal behavior and occasionally seizures. Studies done on humans (which currently only involve the use of 2D ultrasound) has not demonstrated harm... it only has only shown that increased exposure causes increased rates of left handedness in boys... which does imply that there is some impact on the fetal brain... whether or not it's problematic is up for debate....
Anyways that is the reason why medical guidelines in North America advise physicians and midwives and sonographers to only use ultrasound when medically indicated and to limit exposure as theoretical risks due in fact exist and subsequently that also means advising against recreational ultrasounds (many care providers are unaware of these guidelines sadly but if interested they are posted to be viewed by the public at the websites of the Society of Obstetricians and Gynecologists, the American Congress of Obstetricians of Gynecologists, the American Institute of ultrasound etc). Also, because of this there are strict guidelines as the to the power used to generate images (the higher the power the better the pic however) and there are strict guidelines as to how long ultrasound should last with each Mhz and how the ultrasound should be conduct eg the transducer should never remain still as that concentrates the beams in one locations which increases the risk.... Because of all this, there have been some states in the United States which have banned the use of recreational 3D/4D ultrasound and there are several more states in the US and provinces in Canada rallying to do the same.
Now back to dopplers..... as mentioned before they use sound waves much less powerful then that ultrasound... and since major risks of ultrasounds in humans is still theoretical the risks of using a doppler is theoretical as well and because the power used is much less it's probably safer then routine u/s use..... BUT there hasn't been any studies on daily use of dopplers and their is a theoretical possibility that excessive use of dopplers can have a cumulative effect which has the potential to cause brain abnormalities.... And that is why the warning exists.
Ofcourse it's your baby and your body and you everyone has the right to make their own decisions.... Sometimes relieving anxiety is the best decision just like some women need to take anti-anxiety medications when pregnant.... they have risks to baby BUT the benefits can outweight those risks in some cases....
And if you'd rather be on the safe side and skip exposuring baby to excessive amounts of ultrasound waves, after 20 weeks you can use a fetoscope or even a stethoscope. It's the least invasive tool to listen to baby. I fidn it much easier to use after the 25 week mark (though you can hear it before it just takes a quiet room and some more time) and if you're "morbidly obese" it can make listening more difficult but for the average person it works just fine. The trick to using one of those is the best sound is transmitted through the ear piece if the fetoscope is placed on the babies back.. Can take some time for the inexperienced to figure that part out but with some practice it can also be a great tool for helping you determine babies position as well... Fetoscopes tend to be quite cheap and you can get them off ebay or medical supply stores for as little as $15... which I think is about 10 pounds.