Like any relationship, sustained funding requires effort. Grants administration is a continuing process that is sometimes tedious and full of headaches, sometimes harrowing, and sometimes just plain annoying. However, if done right, with a modicum of organization, it can be very worth while. Many agencies such as the U.S. National Science Foundation (NSF), and Department of Defense (DoD), require regular reporting, as I discussed last time. A section documenting published results from prior support is also standard on NSF and NIH funding proposals.
Following through has more advantages than building up your documentation of prior support and research activity, though: it can actually help you augment your funding before you even go to write a new proposal.
One of the most NSF Research Experiences for Undergraduates (REUs) and Research Experiences for Teachers (RETs). If you are a lead PI or co-PI on a major NSF-funded project, such as an Information Technology Research (ITR) project, you can apply for a supplement award. These are usually $3000 to $30000 and cover only funds for the "participant costs", i.e., stipends, of students and (secondary education) teachers who will travel to your host institution to take part in summer research programs. These are usually of 6-12 week duration.
Unlike the standalone site proposals, those for REU and RET supplements are reviewed by the program manager, who makes a summary merit and award decision. The NSF is very strongly committed to "broader impacts" in education and technology transfer, so for many major programs, REU and RET awards are automatic if they can be properly justified and a complete program plan, timeline, and recruiting strategy laid out in advance. Note: NSF will also consider REU programs where the undergraduate intern candidates have already been identified. Nowadays, a 50-50 balance between available candidates and new recruits seems to be preferred, meaning that you may have to conduct a nationwide search (see below).
For an example of an NSF REU, see the web site and announcement for our summer, 2003 REU in Bioinformatics which hosted six students, four of them supported by the NSF and the other two supported by our Summer Undergraduate Research Opportunities Program (SUROP). This one was an REU supplement to an inter-university Plant Genome Research Program (PGRP) grant.