I don't understand what you mean by "Diagnosed with EF"
EF is normally the short form of the therm Ejection Fraction, which is essentially the amount blood that your heart pumps out on every beat compared to how much it could pump out.
A low EF is a symptom of many conditions of the heart, but they are lumped together in one catch all called Congestive Heart Failure and may include thickening of the heart muscle (hypertrophy) or tissue damage from a heart attack, or inflammation of the heart or the pericardium, or coronary artery disease to name a few.
Your doctor will have given you a strict regimen to ensure that the condition that is causing the low ef gets no worse, making sure that the already low EF gets no worse. That is the primary goal ... stop the heart disease from getting worse. Depending on the particular heart problem that lead to a low EF, your EF *may* improve and that is good, but the important thing is to ensure that it gets no worse!
Here's an interesting article on what causes a low EF and what the numbers mean.
http://www.chfpatients.com/faq/ef.htm
Bottom line, don't give up your regimen just because your Ejection Fraction hasn't improved ... it's still saving your life by ensuring that whatever's causing the low EF is not getting worse!
Time and patience will be required. The heart muscle may repair itself to a limited extent, but it takes a very long time.
If that's not what your doctor meant by EF, let us know!