I'm not sure about error, afaik it's something about internet explorer and parsing errors, but.
Dropdown list markup actually generates only once on response, so this string will be constant.
<%= Html.DropDownListFor(model => model.PeriodSelected, Model.PeriodSelectList) %>
will be the same <select>...</select>
all the time.
You need to rethink workflow of your web site to preload all needed information and then work with that only by JavaScript. Thus, you need to filter your periods in browser with javascript and left asp.net mvc only as data source.
Or somehow use ajax to regenerate dropdown list markup on server. In simple words, in ASP.NET MVC you cannot easily mix JavaScript and .NET code. And I think, this is right approach. But, if you want so for some reason:
there're WebForms.