So the sources are being updated continuously? Or just from time to time? You may encounter some locking problems.
One approach could be to move the source file to another folder, import it and then archive it - at least then you know that nothing will write to it while it is being processed, and that you will never process the same thing more than once. Hopefully, whatever is creating the source data will just recreate the file the next time it needs to write data.
You then need a way of monitoring the source folder for new data - in the example above, that just means new files. You could either just schedule the SSIS package to run frequently (exiting gracefully if there are no files to process) or write a Windows service to monitor the folder and run the package in (almost) real time when new files are created.
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