Does 301 redirect always preserve referrer?

I want to know whether 301 redirect always preserve referrer.

I make a page called "gotoorig_https.html" which contains a hyperlink to a page "orig_https.asp".
"orig_https.asp" will 301 redirect to "dest.html" which shows the document.referrer.

In this case,

http page(gotoorig_https.html) -> orig_https.asp(301 redirect)-> https page (dest.html) <--the referrer preserves  
https page(gotoorig_https.html) -> orig_https.asp(301 redirect)-> https page (dest.html) <--the referrer preserves  

I also make a page called "gotoorig_http.html" which contains a hyperlink to a page "orig_http.asp". "orig_http.asp" will 301 redirect to "dest.html" which shows the document.referrer.

In this case,

http page(gotoorig_http.html) -> orig_http.asp(301 redirect)-> http page (dest.html) <--the referrer preserves  
https page(gotoorig_http.html) -> orig_http.asp(301 redirect)-> http page (dest.html) <--the referrer DOES NOT preserve.

Why does the last case happen?