There have been a number of scientific studies addressing the question of how much caffeine is extracted depending on brewing time. Perhaps the most cited is from 1996, but a 2008 study (carried out to debunk the myth that tea can be decaffeinated with a 30-second steep) also gives some useful data with a variety of teas.
To address your question specifically, approximately 70-80% of caffeine is removed, on average, in a 6-minute steep with boiling or near-boiling water. It will vary depending on variety of tea (green, black, etc.) and form (whole black tea leaves release caffeine the slowest; black tea bags containing tea fannings the fastest). Regarding the 30-second “decaf method,” only about 10% of caffeine is released in that short time, so it’s hardly effective. You’d need to steep for at least 5 minutes or so to remove a significant portion of the caffeine.
Given the number above for a 6-minute steep, the maximum amount you could expect to extract from a longer steep for hours or days would be 20-30% of the original caffeine content of the leaves. So you could potentially increase the amount of caffeine in the final brew to maybe 1.25 times of the 6-minute cup or a little more, depending on variety.
However, it should be noted that more than 90% of caffeine will be released by 15 minutes, so steeping for hours or days is not very productive. If, for some reason, you wish to extract the most caffeine from the leaves possible, I would recommend multiple short steeps (5 minutes or less) instead, perhaps with a higher concentration of leaves. Using fresh water periodically will allow faster extraction of caffeine, and you’ll also avoid the inevitable bitterness that generally comes from a single long brewing.
(I should note all of the above regards typical brewing with relatively hot water. Brewing tea with room temperature water or with cold water will significantly increase the time it takes for caffeine to be extracted. In that case, brewing for hours may be necessary to allow large portions of the caffeine to dissolve.)