406: not acceptable response received using LWP::UserAgent/File::Download - perl

Question

Edit: it seems the issue was caused by a dropped cookie. There should have been a session id cookie as well.
For posterity, here's the original question
When sending a request formed as this
GET https://<url>?<parameters>
Cache-Control: max-age=0
Connection: keep-alive
Accept: text/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0.8
Accept-Charset: iso-8859-1,utf-8,UTF-8
Accept-Encoding: gzip, x-gzip, deflate, x-bzip2
Accept-Language: en-US,en;q=0.5
If-None-Match: "6eb7d55abfd0546399e3245ad3a76090"
User-Agent: Mozilla/5.0 libwww-perl/6.13
Cookie: auth_token=<blah>; __cfduid=<blah>
Cookie2: $Version="1"
I receive the following response
response-type: text/html
charset=utf-8
HTTP/1.1 406 Not Acceptable
Cache-Control: no-cache
Connection: keep-alive
Date: Fri, 12 Feb 2016 18:34:00 GMT
Server: cloudflare-nginx
Content-Type: text/html; charset=utf-8
CF-RAY: 273a62969a9b288e-SJC
Client-Date: Fri, 12 Feb 2016 18:34:00 GMT
Client-Peer: <IP4>:443
Client-Response-Num: 10
Client-SSL-Cert-Issuer: /C=GB/ST=Greater Manchester/L=Salford/O=COMODO CA Limite
d/CN=COMODO ECC Domain Validation Secure Server CA 2
Client-SSL-Cert-Subject: /OU=Domain Control Validated/OU=PositiveSSL Multi-Domai
n/CN=ssl<blah>.cloudflaressl.com
Client-SSL-Cipher: <some value>
Client-SSL-Socket-Class: IO::Socket::SSL
Client-SSL-Warning: Peer certificate not verified
Client-Transfer-Encoding: chunked
Status: 406 Not Acceptable
X-Runtime: 9
I'm not entirely sure why the response is 406 Not Acceptable. When
downloaded with firefox, the file in question in 996 KB (as reported
by Windows 8.1's explorer). It looks like I have a partially
transferred file from my perl script at 991 KB (again, windows
explorer size), so it got MOST of the file before throwing the Not
Acceptable response. Using the same URL pattern and request style, I
was able to successfully download a 36 MB file from the server with
this perl library and request form, so the size of the file should not
be magically past some max (chunk) size. As these files are being
updated on approximately 15-minute intervals, I suppose it's possible
that a write was performed on the server, invalidating the ETag before
all chunks were complete on this file?
I tried adding chunked to Accept-Encoding, but that's not for
Transfer encoding and it appears to have no affect on the server's behavior. Additionally, as I've been able to download larger files
(same format) from the same server, that alone shouldn't be the cause
of my woes. LWP is supposed to be able to handle chunked data
returned by a response to GET (as per this newsgroup post).
The server in question is running nginx with Rack::Lint. The
particular server configuration (which I in no way control), throws
500 errors on its own attempts to send 304: not modified. This
caused me to write a workaround for File::Download (sub
lintWorkAround here), so I'm not above putting blame on the
server in this instance also, if warranted. I don't believe I buggered
up the chunk-handling code from File::Download 0.3 (see diff),
but I suppose that's also possible. Is it possible to request a
particular chunk size from the server?
I'm using LWP and libwww versions 6.13 in perl 5.18.2.
File::Download version is my own 0.4_050601.
So, what else could the 406 error mean? Is there a way to request that
the server temporarily cache/version control the entire file so that I
can download a given ETag'd file once the transfer begins?