Here's what's going on with the noticed odd-good/even-bad behavior: 
#!/usr/bin/perl

use common::sense;
use AnyEvent::HTTP;
use Data::Dumper;

sub do {
    my $iter = shift;

    my $cv = AnyEvent->condvar;
    $cv->begin;
    http_get
        'https://imasheep.hurrdurr.org/category/about.html',
        timeout => 2,
        # out-comment to get the even/odd behavior
        persistent => 0,
        sub {
            my ($body, $hdr) = @_;
            say "$iter $hdr->{Status}";
            unless ($hdr->{Status} == 200) {
                warn Data::Dumper->Dump([$hdr],['hdr']);
            }
            $cv->end;
        }
    ;
    $cv->recv;
}

for (1..4) {
    &do($_);
    sleep(5);
}

[download]
The documentation for that 'persistent' reads as follows: 
        persistent => $boolean
               Try to create/reuse a persistent connection. When this flag is set (default: true for idempotent
               requests, false for all others), then "http_request" tries to re-use an existing (previously-created)
               persistent connection to the host and, failing that, tries to create a new one.

               Requests failing in certain ways will be automatically retried once, which is dangerous for non-
               idempotent requests, which is why it defaults to off for them. The reason for this is because the bozos
               who designed HTTP/1.1 made it impossible to distinguish between a fatal error and a normal connection
               timeout, so you never know whether there was a problem with your request or not.

               When reusing an existent connection, many parameters (such as TLS context) will be ignored. See the
               "session" parameter for a workaround.
This default persistence for idempotent requests conflicts with your 5 seconds sleeps - and that's why only every second connection attempt succeeds.


Krambambuli
---

In reply to Re: AnyEvent timers by EV by Krambambuli
in thread AnyEvent timers by EV by bash

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.