Please show your ActiveSync settings in sogo.conf and your reverse proxy (Apache or nginx).

SOGo (anything else needed?):

WOPort = 127.0.0.1:20000;
SOGoEASDebugEnabled = YES;
WOMaxUploadSize = 15360;
SOGoMaximumMessageSizeLimit = 15360;
WOWorkersCount = 10;
SxVMemLimit = 500;
SOGoXSRFValidationEnabled = YES;

WOWatchDogRequestTimeout = 60;
SOGoMaximumPingInterval = 360;
SOGoMaximumSyncInterval = 360;
SOGoInternalSyncInterval = 60;
SOGoMaximumSyncResponseSize = 512;
SOGoMaximumSyncWindowSize = 100;

Also tried with this tune:

WOWatchDogRequestTimeout = 10;
SOGoMaximumPingInterval = 354;
SOGoMaximumSyncInterval = 354;
SOGoInternalSyncInterval = 30;
SOGoMaximumSyncResponseSize = 512;
SOGoMaximumSyncWindowSize = 256;

NGINX:
location ~ ^/sogo { rewrite ^ https://$host/SOGo; }
location ~ ^/SOGO { rewrite ^ https://$host/SOGo; }

Redirect /mail to /SOGo

#location ~ ^/mail { rewrite ^ https://$host/SOGo; }

For Mac OS X and iOS devices.

rewrite ^/.well-known/caldav /SOGo/dav permanent;
rewrite ^/.well-known/carddav /SOGo/dav permanent;
rewrite ^/principals /SOGo/dav permanent;

location ^~ /SOGo {
include /etc/nginx/templates/hsts.tmpl;

proxy_pass http://127.0.0.1:20000;

# forward user's IP address
proxy_set_header X-Real-IP $remote_addr;
proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
proxy_set_header Host $host;

# always use https
proxy_set_header x-webobjects-server-port $server_port;
proxy_set_header x-webobjects-server-name $host;
proxy_set_header x-webobjects-server-url  https://$host;

proxy_set_header x-webobjects-server-protocol HTTP/1.0;

}

location ^~ /Microsoft-Server-ActiveSync {
proxy_pass http://127.0.0.1:20000/SOGo/Microsoft-Server-ActiveSync;

proxy_connect_timeout 3600;
proxy_send_timeout 3600;
proxy_read_timeout 3600;

}

location ^~ /SOGo/Microsoft-Server-ActiveSync {
proxy_pass http://127.0.0.1:20000/SOGo/Microsoft-Server-ActiveSync;

proxy_connect_timeout 3600;
proxy_send_timeout 3600;
proxy_read_timeout 3600;

}

location /SOGo.woa/WebServerResources/ {
alias /usr/lib/GNUstep/SOGo/WebServerResources/;
expires max;
}
location /SOGo/WebServerResources/ {
alias /usr/lib/GNUstep/SOGo/WebServerResources/;
expires max;
}
location ^/SOGo/so/ControlPanel/Products/([^/])/Resources/(.)$ {
alias /usr/lib/GNUstep/SOGo/$1.SOGo/Resources/$2;
expires max;
}
location (^/SOGo/so/ControlPanel/Products/[^/]UI/Resources/..(jpg|png|gif|css|js)$) {
alias /usr/lib/GNUstep/SOGo/$1.SOGo/Resources/$2;
expires max;
}

Also tried to tune mysql with:
max_allowed_packet = 64M

And dovecot with:
imap_max_line_length = 2m

Try without SOGoMaximumSyncWindowSize in sogo.conf and recreate the account on a problem device.

@tfu, thank you for suggestion, that actually works! Thank you very much!

According to SOGo document:

########
SOGoMaximumSyncWindowSize

Parameter used to overwrite the maximum number of items returned during a Sync operation.

Defaults to 0, which means no overwrite is performed.

Setting this parameter to a value greater than 512 will have unexpected behaviour with various ActiveSync clients.
#######

With "SOGoMaximumSyncWindowSize = 256;", Android OS 5/7 cannot sync contacts. It doesn't reach the "512" limit as mentioned in doc. So what's the recommended setting? Simply use default setting, or we need a tuning in some cases?

AS you have set SOGoMaximumSyncResponseSize, you do not need to limit with SOGoMaximumSyncWindowSize too.
SOGoMaximumSyncWindowSize is for limiting how many objects are synchronized in on go at max.
SOGoMaximumSyncResponseSize limits the maximum size of one synchronization round.
So only as many objects as fit in that size will be transfered, or 1 object at a time, if greater than the given limit.

So we'd better use either one for limit? And which one is better? ResponseSize or WindowSize? What's the "always working" setting?

As object size is differing wildly (e.g. email with attachment versus one event). the ResponseSize is the restriction with better results.
You have a faster synchronization for small objects, while preventing too huge responses (and response times) for bigger ones.

In my experience this works good, but I didn't test the other one as explicitly, so it probably works equally good.