I think it really just depends on the person. The monitor does take about 3 months to "adjust" to your individual cycle. Are you taking any meds? When I take Clomid I get at least 5 High readings. But, since I know my schedule better now, I save a lot of sticks by only testing a few days around O.
To sum up my answer- I don't think it's abnormal to get so many high readings. You may not get a peak reading, but that doesn't mean you didn't/won't O. You might want to temp, if you're not already- just as a confirmation for O.