An image in your email signature can become unsharp when sending even when it still looked sharp when composing.
The cause of this issue lies in the way Outlook on Windows handles your image in combination with its dpi value.
Outlook will rescale the image as if it was a 96 dpi image. It gets worse - Upon sending, Outlook will convert and compress (re-render) the images to 96 dpi with the new dimensions.
Re-render the image at 96 dpi
The quickest and easiest way around this issue is to re-render your images at 96 dpi.
In general, this will not produce a noticeable quality loss.
Right-click the image file and verify it's 96 dpi.
Select Properties and Details tab: