loss of color profile exporting from photoshop

I recommend users to "save as" rather than export. but either way you need to be sure that 'embed icc profile' is checked.

For some inexplicable reason, it's not set as default in export. 

I hope this helps
neil barstow, colourmanagement net :: adobe forum volunteer:: co-author: 'getting colour right'
google me "neil barstow colourmanagement" for lots of free articles on colour management

What's wrong is that the checkbox to "embed profile" in Export (and Save For Web) is unchecked by default. You have to check this box manually.

Save As will always embed the profile.

Yes, the image should always have an embedded profile. Without it, the colors are undefined and will display randomly according to outside factors which can vary.

Export:

Save For Web:

In SFW there's an extra "preview" setting that you need to watch, or you'll get the non-color managed version and it won't match Photoshop. This preview setting is baked into Embed Profile in Export.

I've moved this from the Using the Community forum (which is the forum for issues using the forums) to the Photoshop forum so that proper help can be offered.