Hi , I`m JackPerhaps I can help you with this problem , a few questions coming up and please note that it may take a few minutes between replies;
What is this downconverter , hdmi to composite or component video for example ?
Does it have a model number ?
In that case go in your Roku`s setup menu and lower its output resolution to 720p for example or as much as you can , its coming out of the converter at 480i anyway so that wont make a difference on the picture quality but certainly would make a difference in the ease of streaming wifi if that is the problem and also probably would make life easier for that converter .
Give it a try and if that does the trick then please do not forget to rate by clicking on the star icons at the top, then click on Submit so i get paid for my time helping you .Also note that it will not close this post , you can come back here at any time if you need further info or help . Thank you
By the way , if that converter also has standard (composite) video out , give it a try