Gaussian Blur preview is slow to calculate
Gaussian Blur is just so difficult to use, and preview NEVER works.
When it's activated, to make a change on the objects or font that it is applied to, requires that I always turn it off first and turn it back on later. There is always a long delay for it to appear. The Gaussian blur needs to be redesigned so it is as dynamic and powerful as the feature in Photoshop.

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It explains it, yeah. Even though you never said how large your blurred objects — I mean length units. It matters. The file size of links in MB matters less.
I can imagine Photoshop would start to choke with this amount of smart objects too, with live gaussian blur applied, given the 300 ppi resolution!
300 is way to much for drafting in most cases. Try to set a smaller value, just to see the differences in the quality and the calculation speed. Even though the team recently made some changes to make blur faster, to use multiple threads of a processor, it’s not magic, and Gaussian Blur, being simple, is actually a very heavy and ineffective algorithm in its core.I can explain the file size problem as well. When you save, Ai enables the Create PDF Compatibility File option. And it basically writes the full PDF copy each time you save. And the more images you put into the document, and the more blur you add, the slower the saving process. This option is useful for recovery purposes (if the native PGF format Ai uses fails, Ai can try to import the PDF part of the document). Also this allows for the document to be placed into Photoshop or InDesign — they read this PDF portion only... but for drafting purposes it’s BAD. It takes up space, it takes the time... Try to Save As, disable the option, and see if the time and size change.
If possible, having a look into the actual file would help the team to iterate more on the performance. If you are OK with it — please collect it all using File > Package, and send the link to the zipped folder to sharewithai@adobe.com — please also mention the link to this report, so they can track it back — http://illustrator.uservoice.com/forums/601447/suggestions/50355072
In any case, please comment back if changing the compatibility option and changing the resolution do anything.
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Nikki commented
So, the blur is active on a a grouped object, a series of 8 small rectangles that also contains clipped images. Also the document contained 40+ clipped images that link to PSD or PNGs, but each one no more than 10 MB. But when I'm drafting, I duplicate images and use them in different ways as I brainstorm. When this happens, the AI file becomes very large, like over 1 GB, and then very difficult to manage like long time to save and issues like the drop shadow/gaussian blur taking a long time and being hard to handle.
When I pare down the document, at the point that I"m finalizing a design, these issues are much better. It's when the file is heavy that a lot of the issues happen and it's frustrating.
My document raster settings are always at 300 dpi.
Anyway hope that helps.
I hope that helps.
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Nikki, how large is the object you apply the blur to? Please share the dimensions.
How large is the resolution for raster effects the document uses (Effect > Document Raster Effects Settings)?
How do you try to edit the effect specifically? —please provide steps or record a short video.