Thanks to help from Customer Support at National Instruments, we found the cause for this problem, and a workaround.
The problem can be boiled down to the following: When setting the stop condition to continuous, the number of scans to a high number (eg 840000), and the progress interval to a short number (eg 300), the "start" instruction takes tens of seconds to complete.
This misbehavior must have to do with the NIDAQ 6.9.3 or with Measurement Studio or with Win XP, because it did not appear in NIDAQ 6.1 with ComponentWorks 2.0 in Win NT 4.0.
A very useful visit from a National Instruments representative yielded a simple workaround: do not use continuous acquisition. Now we simply specify a long buffer and we set the stop condition to "no condition", and
everything seems to work fine.