drsosc is a graphical application contiously acquiring data from the board, and drscl is a command line tool for debugging, as written in the manual.
The drsosc application runs indefinitely, but I guess you refer to saving data (by hitting the "Save" button in the drsosc application). Yes the save functionality has a number of events, since you cannot store data indefinitely, since your harddisk does not have indefinite space!
I kind of sense that you want to convert the "number of event to save" into "number of seconds or hours to save". This is not build into the drsosc application. It's all open source, so feel free to change the code. Alternatively, you can use the drs_exam.cpp program coming with the distribution, wich is a simpel C++ program reading the board. It has a for loop over 10 events, but you can change the code easily to run for a predetermined amount of time.
Am I correct in assuming that drsosc and drscl are functionally equivalent regarding collecting data? We want to run the DRS4-EB for a predefined amount of time. However, the DRS4 scope application seems only to run for a predefined set of measurements. Have I got that right? Is there some reason to avoid running the DRS4-EB for a predefined amount of time that I should be aware of?