A single process, if heavily used, can overtax the processor in this unit resulting in reported failures when trying to access the unit through other means. In other words, depending on how you access the unit, you can certainly cause delays that will result in processes failing.
I have 3 DNS-323's that I use for various purposes. I do however try and restrict any disk writing activity that is heavy (as a full backup would be) to a sinlge occurance at a time as I have seen failures as you describe. Installing a shell and monitoring with 'top' is an easy way to see the requests getting queued. If the software can't handle the delays, then there can be failures.
I used to 'push' backups onto the units. What I do now is 'pull' them instead. This allows the NAS to work at its own pace and sequencially perform the backups.