Most likely you have to connect the DVD drive via a powered USB hub.
Maximum USB current on RPis is 1.2A - for all 4 ports combined. If you exceed that (eg if the DVD drive or a USB HDD needs more when spinning up) you'll get the symptoms you described (USB reset, devices "falling off the bus").
See also the RPi FAQ FAQs - Raspberry Pi Documentation
QuoteFrom the Raspberry Pi B+ onwards, 1.2A is supplied to downstream USB peripherals. This allows the vast majority of USB devices to be connected directly to these models, assuming the upstream power supply has sufficient available current.
Very high-current devices, or devices which can draw a surge current such as certain modems and USB hard disks, will still require an external powered USB hub.
so long,
Hias