for now the only way to renew the plugins update info is to follow this steps:

[jenkins@ci]# wget -O default.js http://updates.jenkins-ci.org/update-center.json
[jenkins@ci]# sed '1d;$d' default.js >  /var/lib/jenkins/updates/default.json

Sounds an issue of core, not updatesite-manager plugin (you don't look use updatesite-manager plugin at all).
Changed component/s.

Click the button, then https://wiki.jenkins-ci.org/display/JENKINS/Obtaining+a+thread+dump

It's possible it's a network connectivity issue, with Jenkins configured (proxies?) to not reach our update sites.

i have attached one threadDump just right when i click botton, and another dump is after a while

i have not proxies in between (just usual NAT) and i can download manually the default.json file from inside the jenkins machine

Weird, no threads there.

Any notable error responses when you check your browser's dev console, after clicking Check Now?

GET-request.txt.zip postBack.txt.zip

yes, actually there is an postback error when sniffering through dev console:

1. On GET request https://updates.jenkins-ci.org/current/update-center.json.html?id=default&version=2.53
The headers are:

Accept:text/html,application/xhtml+xml,application/xml;q=0.9,image/webp,*/*;q=0.8
Accept-Encoding:gzip, deflate, sdch, br
Accept-Language:en-US,en;q=0.8,ru;q=0.6,zh;q=0.4
Connection:keep-alive
Host:updates.jenkins-ci.org
If-Modified-Since:Fri, 14 Apr 2017 05:32:56 GMT
If-None-Match:"117316-54d19c619320f-gzip"
Referer:http://jenkins.vm.mycorp.local/pluginManager/checkUpdates
Upgrade-Insecure-Requests:1
User-Agent:Mozilla/5.0 (Windows NT 6.1; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/57.0.2987.133 Safari/537.36

And the whole request body file-attached as : GET-request.txt.zip (it has json pretty-formatted for readability)

2. And then i'v got a respone with Status Code:413 Request Entity Too Large.
And the whole response body file-attached as postBack.txt.zip (it has json pretty-formatted for readability)

Thank you for the tips. I have it fixed by configuring client_max_body_size of the nginx:

# vi /etc/nginx/sites-enabled/jenkins
server {
    client_max_body_size 10m;
...

# service nginx restart

this parameter is also documented here https://wiki.jenkins-ci.org/display/JENKINS/Running+Jenkins+behind+Nginx

The browser-based metadata download has been deprecated as being unsafe and unreliable years ago. There should have been an admin monitor warnings against its use. Seems you dismissed it?

i actually dont remember. it is possible i somehow mute it. And now what should i do?

Well, you worked around it. Nothing I suppose? But you can still disable the option in the security configuration.