Cannot change password from Oracle EM
That's not the best practice to use SYS user to use in Enterprise Manager. And you can change password for the user like SYSTEM or SYSMAN using OEM but not for SYS user.

You can change the password of SYS user using SQL*PLUS command called password which send the password in encrypted form instead of plain text.

[oracle@ora12c ~]$ sqlplus sys@oracdb as sysdba

SQL*Plus: Release 12.1.0.2.0 Production on Tue Jan 24 13:37:49 2017

Copyright (c) 1982, 2014, Oracle.  All rights reserved.


Connected to:
Oracle Database 12c Enterprise Edition Release 12.1.0.2.0 - 64bit Production
With the Partitioning, Automatic Storage Management, OLAP, Advanced Analytics
and Real Application Testing options

SQL&gt; password
Changing password for SYS
Old password: 
New password: 
Retype new password: 
Password changed


First of all find out which profile is assigned to the user-

SQL&gt; select profile from dba_users where username='SYS';

PROFILE
--------------------------------------------------------------------------------
DEFAULT


-then you can user ALTER PROFILE to change password life time. 

Also password doesn't cause effect on SYS user(I couldn't find documentation link) as demonstrated below.

SQL&gt; alter user sys password expire;

User altered.


But I still can connect to the database using old password. 

C:\Users\user&gt;sqlplus sys/oracle@192.168.30.133:1522/oracdb as sysdba

SQL*Plus: Release 11.2.0.4.0 Production on Tue Jan 24 13:52:46 2017

Copyright (c) 1982, 2013, Oracle.  All rights reserved.


Connected to:
Oracle Database 12c Enterprise Edition Release 12.1.0.2.0 - 64bit Production
With the Partitioning, Automatic Storage Management, OLAP, Advanced Analytics
and Real Application Testing options


However, if your password for sys user has expired and unable to login then-
 use ORAPW utility
 run sqlplus / as sysdba from the terminal of the user who owns the Oracle software.