Does the website http://www.speedtest.net enforce any limit on the number of speed tests from a given IP? (e.g. max 1000 tests per day)
There shouldn't be.
After examining their website, there is no language saying that there are a predefined number of tests you can do in a certain time period.
However, with that said, if they discover that you're doing something they don't like they can blacklist your IP address at their jurisdiction.
Short answer, No. Just don't end up on anyone's blacklist.