Annoying noise appears when I export my tracks.

I am not a Breverb user, but I'd diagnose this the same way as with any other suspected plugin - starting by verifying that the plugin is indeed at fault, and then examining the waveform to determine the type of artifact.

Do the artifacts disappear if you bypass the reverb before exporting?  
 
Are they still there if you substitute a different reverb plugin? 

Have you brought the exported track back into SONAR to examine closely and identify the nature of the noise/distortion?

If Breverb has an oversampling option, does that setting make any difference?

What's the signal level at the output of the master bus? Have you eliminated clipping at the interface?

Do symptoms change or disappear if you freeze your tracks before exporting?

Does exporting with larger audio buffers (higher latency) make a difference? What size buffers are you using now?

Dropouts can sound like severe distortion. They are the result of interruptions to the data stream when the CPU doesn't have enough time to process each outgoing buffer-full of data and can't keep the output buffers filled. Raising buffer sizes can alleviate that. You can also have similar effects if the disk drive can't keep up or if you're close to exhausting RAM, both usually only a problem with samplers.

And, of course, there is the possibility of real distortion due to clipping. This, however, is normally rare if you follow reasonable practices with regard to levels. And it's rarely caused by an effect plugin.