Based on your description it sounds like you might be having more disconnection issues as of late. Right now it is important to be aware if there is anything hindering between you and the game server. For example, AT&T and Comcast subscribers nationwide have critical issues that affect services like online gaming in the last couple of days. Blizzard has been monitoring this but there is not much they can do from their end. Of course, there can always be other factors at work.
If you are disconnecting more often (where you get the “Lost Connection to the Server” error message), first please take the time to make sure everything on your end is working correctly (click here), even if your general internet connection is not dropping. If the troubleshooting doesn’t help, consider running a WinMTR test (click here). It is a great method to actively test your connection as you play and look for problems between you and the game server. Post the results in the technical support forum and assistance with the results of the test can be provided.
If you are crashing more often (where the game client closes entirely), something is going on with the computer that can interfere with Overwatch, without additional information from you, I can only recommend these standard troubleshooting steps (click here).
As always all crashes and disconnections will count as leaving the game and will be penalized appropriately. This is important to ensure the overall community is not too impacted with leavers (regardless if they leave intentionally or not). You can learn more about this policy in this post from Blizzard (click here). Please make every effort to avoid Competitive Play until you are extremely confident the issues that affect you are resolved.