We are carrying out a survey of magnetic fields in Ap stars in open clusters in order to obtain the first sample of magnetic upper main sequence stars with precisely known ages. These data will constrain theories of field evolution in these stars. Using the new spectropolarimeter ESPaDOnS at CFHT, we have obtained 44 measurements of the mean longitudinal fields of 23 B6 - A2 stars that have been identified as possible Ap stars and that are possible members of open clusters, with a median uncertainty of about 45 G. Of these stars, 10 have definite field detections. Nine stars of our sample are found not to be magnetic Ap stars. The ESPaDOnS data contain a large amount of useful information not readily obtained from lower resolution spectropolarimetry. With the new observations we are able to expand the available data on fields of low-mass, relatively evolved Ap stars, and identify more robustly which observed stars are actually magnetic Ap stars and cluster members. Re-analysis of the enlarged data set of cluster Ap stars indicates that such stars with masses in the range of 2 -- 5 mo show RMS fields larger than about 1 kG only when they are near the ZAMS. The time scale on which these large fields disappear varies strongly with mass, ranging from about 250 Myr for stars of 2 - 3 solar mass to 15 Myr for stars of 4 - 5 solar mass. Our data are consistent either with emergent flux conservation for most (but not all) Ap stars, or with modest decline in flux with age.