soxfan, I've had this same symptom on and off for over 20 years, even before my CFS became a serious problem. Over that time I have learned a lot, and been evaluated many times. In fact just had an EKG last week again. And no serious heart problems. However I do have some clues from all the different attempts at treatment. Beta blockers help but are not curative. I don't like being on the drugs due to the side effects. The most helpful thing I have learned/found was from studying Dr Bell's research and most recently Prof. Pall's hypothesis about nitric oxide (NO) problems in CFS (NO helps regulate blood pressure/volume, among other things). To make a long story short, CFS can involve low blood volume (hypovolemia), in some CFS patients it is lower than the level at which healthy people die of shock from blood loss. As the blood volume goes down, the heart must work harder to keep circulation levels required to sustain life. Bell and Pall believe this is caused by a regulation mechanism failure involving barorecepters (pressure/stretch sensing nerves in the arteries and some veins). There may be other explanations, but regardless of the cause, this is a normal part of CFS for some of us. It is nothing to get alarmed about, but you can do things to help treat the problem. Rehydration drinks that you can tolerate are important (keep up blood volume), managing stress and exertion levels (both of which appear to cause blood vessels to clamp down in CFS and thus lower blood volume), and finding ways to treat the strange hypertension we seem to have (wired but tired). I have found a number of natural treatments that seem to help with NO management and work as well as any BP medication I have ever tried, in fact some natural substances work for me better than beta blockers. I don't think there is a universal treatment, you have to study and find what works for you. In my case bioflavonoids make a huge difference as some are vasodilators, just for example. And I make my own rehydration drink, so I can control the ingredients and make sure I tolerate it well. Some supplements I use help calm my nerves and that makes a difference. Also I use a multi B12 supplement protocol that is similar to Pall's recommends and seems to help manage the NO/ONOO- situation he describes. And practicing mold avoidance really has helped reduce this particular symptom, mold must aggravate the NO/ONOO- problem, or something related to blood volume.
There are ways to help this situation, but most doctors are not going to go beyond trying a few drugs, which is not enough for this type of pathology in my opinion. Fortunately my primary care doc knows enough about CFS to respect its complexity, but I've had docs before who did not and frankly were dangerous. Hope you find some help.