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Memory Leaks beskrives således

When any program begins running, it uses up some space in the "system resources" area in memory. But, as you exit, some programs do not give back system resources they were temporarily using. Eventually the system will crash as it runs out of memory. The crash happens sometimes if you start and close many programs, even the same ones, without a periodic reboot. This is what Microsoft calls a resource leak or memory leak.

Normalt forstår jeg Memory Leaks son noget programmer laver, hvis de er dårligt programmerede. Jeg vil tro at han taler om at du skal afslutte dine connections ordentligt, som du jo selv er inde på.

Som jeg også skriver: "Jeg har altid lukket mine db-connections efter brug, men jeg har ikke altid lukket mine recordsets efter brug..." Spiller det nogen rolle at jeg ikke lukker mine recordsets?

Normally, or at least in VB/VBA a recordset will get closed when it goes out of scope. This mean that if you open a recordset in a functionthen as soon as you exit the function it should get closed and the memory freed. Even so it is ALWAYS a good idea to close your connections and code after use, it makes good programming.
What puzzles me is you say you close your connection but NOT your recordset. Well normally you would close things in the reverse order as to what you opened them in. So you would first close your recordset (which is using the connection) and then close the connection.