You mistake the purpose of the persistent connection. It allows you to make multiple requests and get multiple responses over one connection.
In your test, you send one request and you're trying to provide an unlimited length response body.
The way you try to provide unlimited length response body is not correct. Please read this RFC, paying special attention to "transfer coding". Some choice quotes:
Persistent connections in HTTP/1.0 are
explicitly negotiated as they are not the default behavior. HTTP/1.0
experimental implementations of persistent connections are faulty,
and the new facilities in HTTP/1.1 are designed to rectify these
problems.
...
Persistent connections are the default for
HTTP/1.1 messages; we introduce a new keyword (Connection: close) for
declaring non-persistence. See section 14.10.
...
7.2.2 Entity Length
The entity-length of a message is the length of the message-body
before any transfer-codings have been applied. Section 4.4 defines
how the transfer-length of a message-body is determined.
...
4.4 Message Length
The transfer-length of a message is the length of the message-body as
it appears in the message; that is, after any transfer-codings have
been applied. When a message-body is included with a message, the
transfer-length of that body is determined by one of the following
(in order of precedence):
...
2.If a Transfer-Encoding header field (section 14.41) is present and
has any value other than "identity", then the transfer-length is
defined by use of the "chunked" transfer-coding (section 3.6),
unless the message is terminated by closing the connection.
3.If a Content-Length header field (section 14.13) is present, its
decimal value in OCTETs represents both the entity-length and the
transfer-length. The Content-Length header field MUST NOT be sent
if these two lengths are different (i.e., if a Transfer-Encoding
header field is present). If a message is received with both a
Transfer-Encoding header field and a Content-Length header field,
the latter MUST be ignored.
4.If the message uses the media type "multipart/byteranges", and the
ransfer-length is not otherwise specified, then this self-
elimiting media type defines the transfer-length. This media type
UST NOT be used unless the sender knows that the recipient can arse
it; the presence in a request of a Range header with ultiple byte-
range specifiers from a 1.1 client implies that the lient can parse
multipart/byteranges responses.
A range header might be forwarded by a 1.0 proxy that does not
understand multipart/byteranges; in this case the server MUST
delimit the message using methods defined in items 1,3 or 5 of
this section.
5.By the server closing the connection. (Closing the connection
cannot be used to indicate the end of a request body, since that
would leave no possibility for the server to send back a response.)