Miriel,
My first impression is that since the target feature class has a resolution of .000000001, this probably should be fine and this is not the cause of the problem you are experiencing.
It appears that your target feature class is in Geographic Coordinates (maybe something like GCS_WGS_1984). Is that correct? If so, is the coordinate system for your ArcMap Data Frame in the same coordinate system?
If it isn't, then as soon as you start editing your feature class you would typically get a warning stating "Spatial reference does not match data frame". If this is the case, then perhaps this could be the problem.
Josh