OK, OK, maybe you guys got lucky and raised some good points. Hmmm...
So I went back to the drawing board and did the following with kombilo:
Searched for "B+" and "W+", thus finding all games won by Black and White respectively. There were 33,003 games and 29,867 games.
Within each of the previous selections, searched for "B+R" and "W+R" for games won by resignation.
In all cases, I also searched on the empty board, which will exclude all handicap games and also all the old Chinese games that began with two White and two Black stones on the board.
The result is this graph.
I also searched for "B+ " and "W+ " (i.e. with an empty space rather than an "R" or a number) to isolate the games with an unclear result. There were 58 such games for Black and 64 for White. How to treat these is, by their nature, unclear. The limiting case is to assume that they are all games decided by resignation. Doing so results in this graph.
There are a few games that end up double counted when there is a comment like - W+ (but another source gives B+). This will be picked up by both the "W+" and "B+" searches. There seemed to be around 45 such games but I could not tell exactly. Most periods had no such games and the highest incidence was 4 out of 964 games in 1850-1899. I ignored the problem since I could not think of a way to exclude them in an automated fashion.
I think we can see a tendency for more games to be decided by resignation over the last ten years. However, we also see that the increase is from a long-term base rate of around 60% up to most recently around 75%. I do not see that this supports the idea that games were primarily played out to the end in previous periods. But as usual YMMV
Edit: Here is the First Graph data adjusted to exclude the games played under Chinese rules (issue raised in later posts below). I searched for "RU[Chinese" to identify the games. I am placing it here for easy comparison. It does not alter the basic trends greatly.
). Here are the results of searching for "B+R" and "W+R" using kombilo and then dumping the numbers into excel. I do not think that the trends we see are tied to the recent introduction of short time limits in tournaments. The major increase for both Black and White looks like it is more likely related to the original introduction of clocks. The steadiness of Black's ratio speaks rather against the influence of changing time limits. Meanwhile the gradual increase for White looks like it is more likely related to changes in komi over the years than time limits. Anyway YMMV, as always! 
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