I think you've mentioned using Opera, and I also remember that Opera (Mini) has a Turbo Mode, where it uses an Opera-operated proxy.

I never use Turbo mode.

Also consider whether Opera gets a different IP address for search.cpan.org than what Perl gets - Perl might end up with an unavailable mirror (sometimes) while Opera might be lucky due to longer DNS caching within the browser (instead of relying on the OS to provide "current" DNS).

Tracking through using TCPView, both LWP and Opera are resolving cpan.strawberryPerl.com:80 to 69.163.152.144, but with LWP the server responds with http error code 500:

Fetching with LWP:
http://cpan.strawberryperl.com/modules/03modlist.data.gz
LWP failed with code[500] message[Can't connect to cpan.strawberryperl
+.com:80]
[download]

So then I discovered I could configure cpan to fall back to wget, and it resolves (presumably the same way as LWP) to the same address, and the fetch immediately works every time:

Running install for module 'Test::Number::Delta'
Fetching with LWP:
http://cpan.strawberryperl.com/authors/id/D/DA/DAGOLDEN/Test-Number-De
+lta-1.06.tar.gz
LWP failed with code[500] message[Can't connect to cpan.strawberryperl
+.com:80]

Trying with
    c:/perl64/bin/wget.exe -O "C:\Perl5.18\cpan\sources\authors\id\D\D
+A\DAGOLDEN\Test-Number-Delta-1.06.tar.gz.tmp11488"
to get
    http://cpan.strawberryperl.com/authors/id/D/DA/DAGOLDEN/Test-Numbe
+r-Delta-1.06.tar.gz
--2014-12-30 18:03:48--  http://cpan.strawberryperl.com/authors/id/D/D
+A/DAGOLDEN/Test-Number-Delta-1.06.tar.gz
Resolving cpan.strawberryperl.com... 69.163.152.144
Connecting to cpan.strawberryperl.com|69.163.152.144|:80... connected.
HTTP request sent, awaiting response... 302 Found
Location: http://cpan.pair.com/authors/id/D/DA/DAGOLDEN/Test-Number-De
+lta-1.06.tar.gz [following]
--2014-12-30 18:03:48--  http://cpan.pair.com/authors/id/D/DA/DAGOLDEN
+/Test-Number-Delta-1.06.tar.gz
Resolving cpan.pair.com... 66.39.76.93
Connecting to cpan.pair.com|66.39.76.93|:80... connected.
HTTP request sent, awaiting response... 200 OK
Length: 21077 (21K) [application/x-gzip]
Saving to: `C:/Perl5.18/cpan/sources/authors/id/D/DA/DAGOLDEN/Test-Num
+ber-Delta-1.06.tar.gz.tmp11488'

100%[=================================================================
+>] 21,077      51.2K/s   in 0.4s

2014-12-30 18:03:49 (51.2 KB/s) - `C:/Perl5.18/cpan/sources/authors/id
+/D/DA/DAGOLDEN/Test-Number-Delta-1.06.tar.gz.tmp11488' saved [21077/2
+1077]
[download]

What appears to be happening, is that LWP is reporting the 302 Found redirection to cpan.pair.com as a 500 message?

Anyway, configuring cpan to use wget means it eventually gets everything required; and popping two of three cpan.pair.com entries from the (default) urllist reduces the noise somewhat.

If anyone has any further suggestions, I'm all ears.