Assimilator1, you're not the 1st. that gets confused by the wording, "Connect every N days", in reality BOINC will normally ask for more work immediately when cached work drops below your cache-setting.
Meaning, after result-1 is finished and uploaded, and sometime during your crunching of result-2, you'll ask for more work.
The reason it doesn't always follow this is, BOINC bases everything after expected run-times, but in reality crunch-times variates some.
Example, if uses 1.5h on VHAR and 2h on "normal" wu, and uses 5-day cache-setting, if you've crunched through a bunch of VHAR the BOINC-client expects ever wu takes 1.5h. meaning 80-81 wu cached. But, immediately after you've finished a "normal" wu, BOINC-client expects wu takes 2h, meaning you've suddenly got 160 hours cached, or 6.666 days. Since 6.666 > 5, you'll crunch 1.666 days, 40h or 20 results before next time asks for more work...
Still, if single-project or 99%-resource-share or something, most of the time you'll ask for more work when you've finished 1-2 results, regardless of 0.2 or 5-days cache-setting.