Disclaimer: Not a Windows specialist, however overall concept should still hold.
VCS 5.0 Administrator's Guide:
http://sfdoccentral.symantec.com/sf/5.0/windows/pdf/VCS_Admin.pdf
Under Resource type attributes, see:
MonitorTimeout (default 60 seconds)
MonitorInterval (default 60 seconds)
What's probably happening is the online program runs and completes succcessfully, then after 60 seconds (MonitorInterval) the first probe runs to check if it's up/running. As the process is not running yet, it times out after 60 seconds (MonitorTimeout), and since it's still not up it fails (hence the 120 second interval).
If the process takes 150 seconds to start, but once it's running you're happy to monitor every 60 seconds (default), look at the OnlineWaitLimit attribute so it will wait X monitorintervals after Online before marking it as failed.
Note: this will affect all Process resources unless you override the attribute for this particular instance (see Admin Guide for details/instructions to do this).
Hope that helps.