Are our calendars inaccurate (even with leap years)?

I was going through Cecil’s archives and came across When do leap-day babies celebrate their birthdays? .

Cecil states “One year = one complete revolution by the earth around the sun = 365 days, 5 hours, 48 minutes, and 46 seconds.”

This got me thinking (since one year did not equal 365 days 6 hours), don’t we gain a few minutes on leap years? Will our calendars one day be horribly out of sync with the earth? According to

this site :

“A solar year (365.2422 days) consists of the period of time (365 days, 5 hours, 48 minutes, and 46 seconds) spent by the sun in making its apparent passage from vernal equinox to vernal equinox. In fact, a solar year is the time it takes the earth to make one orbit about the sun using the instant in the spring when the sun’s center crosses the equator as a reference point. The earth, however, does not circle the sun at a constant rate, nor does the earth rotate on its axis at a fixed rate. The earth revolves faster when it is nearer the sun during the northern winter. The solar year, or the year of the seasons, is about 20 minutes shorter than the true period of the earth’s revolution. The difference is the result of the precession of the earth.”
OK so there’s a bunch of numbers flying around…my basic question is if a year is 365.2422 days, then the extra day added every 4th year is .0312 days longer (1 -.2422*4), or 44.928 minutes longer than the actual year, how do we account for this extra time?