I was able to reproduce the issue. Let me research a little bit on that and I will give you a feedback.
If you want a fast workaround, you can use time=Today-20:14:29.35 instead. It worked for me at least.
Please let me know if this work for you.
I still will provide a feedback about your original issue!
I think I found the issue. You should encode the time string before using it on the URL. Concerning your use case, please try to use &time=Yesterday%2b03%3a45%3a30.25 instead and let us know if this works well on your system.
There are many ways to encode a string. In C#, I have used the HttpUtility.UrlEncode class within the System.Web namespace. You should add the System.Web assembly reference to your .NET project in case you want to get the string returned from this method.
Please let me know if this answers your problem!
Thanks - that works for me, in fact it seems to be sufficient to simply encode the '+'.
I will assume that this is all the needs encoding unless my testing shows otherwise!