Before I could easily find my current location being offline using offline maps but at present in the updated Google maps I am not able to use it. It shows the location while I am online, and once I go offline the location no longer appears. What to do?
To get a location fix while offline, GPS (not just location) needs to be enabled. You must have either "High accuracy" or "Device only" enabled under Settings->Location->Mode. "Battery saving" does not allow use of GPS.
When you are offline, the time to get a location fix is much higher than when you are online.
There are two reasons for this:
WiFi based location is very fast. Without being online, you cannot use WiFi location.
GPS works much faster when you are online, due to the benefits of Assisted GPS. Without Assisted GPS, your GPS receiver needs to do a search for satellites itself which can take a few minutes. GPS also requires sufficient visibility to satellites, so don't try to use GPS while underground or in so-called urban canyons with lots of skyscrapers blocking the sky.
Summary: make sure GPS is on and wait a few minutes in an outdoor space where you can see the sky. Your location should appear.