This request has come to me more than a few times this month. I have checked with my good friends in missionary research, Michael Jaffarian and Bert Hickman (researchers associated with Operation World and the World Christian Encyclopedia) to double-check my own understanding. Here's the consensus:
1. Missionary deployment from the United States is not precisely declining. They've been in the vicinity of 40,000 (on the Protestant side) from the USA (I don't have Catholic sending readily to hand). They peaked around 44,500 in 1988, then declined to about 38,000 around 1992, and after that have shown a slight-but-steady increase since then.
One source for analyzing this is the North American Mission Handbook, which is published about every three years (and another edition is in the works). Update: in this Tweet from Gina Zurlo at the Center for the Study of Global Christianity, she says 127,000 missionaries are sent from the USA. This includes Catholics. I wouldn't do a direct subtract from the 40,000 above, as the two numbers come from two different methodologies and different times, but at least it gives you some idea. Also, the link goes to their report which has sending by continent.
2. Some components of missionary deployment have been declining steadily for years, mainly the number of missionaries sent out by the mainline churches.
3. Many more evangelical missionaries are now being sent out directly through smaller agencies and from individual churches, and these are not showing up in many of the existing statistical measuring systems. I'm not sure how the Mission Handbook will deal with this in the next edition. For some time, however, it's been known that a minority percentage of missionaries do this (for example, I know one missionary family that was rejected from many agencies and so formed their own agency and went--and were quite effective on the field).
4. The statistics I've cited above include people deployed for 4 years or longer. There appear to have been a slight decline in those deployed for 1 month to 4 years (see this daily post) No one measures the short-term trip takers (e.g. 2 weeks), but Michael told me about one study he saw that estimated those at 1.5 million per year.
5. Another factor impacting missionary deployment statistics is longevity on the field; see "Seasons of Transition." People are coming back faster than ever, for a variety of reasons. We wonder why people don't have the "stick-to-it-ness" of those in days gone by, but one possibility is this: the ease of travel means people don't have to make the same kinds of commitment to the field as people had to when it took a year to get to their station.
The bottom line is this: I don't see that the number of missionaries sent from the USA is dramatically declining; in fact, it may very well be growing amongst certain groups. However, neither is it growing dramatically - certainly not to the levels "needed." The West will never field all the missionary workers needed, so we need to think about how to use our existing force strategically to stimulate more workers and more works from other places closer to the harvest.