...people getting injected are still falling ill..

I think all the evidence is that when people fall ill despite having a first jab, they got the virus shortly before or after having the jab. So they became ill before the vaccine had produced an antibody response (which takes about 2 weeks). 

There's a wealth of evidence that the vaccines are very effective. But it takes time for the antibodies to be manufactured and the lymphocytes to be programned. Many people are not aware of this and think they're immune the moment they walk out of the clinic. They relax their usual precsutions and get infected.