Hello,
First of all thanks for choosing our Theme, we are glad to be you in WoodMart WordPress family :-)
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I have test your site by registering myself on your site and I also noticed the same thing on some of your pages we always have to refresh the page with F5 and then it gets the session of logged in user and display “My Account” except of Login/Register option.
Could you please deactivate all the third party plugins(if you have any) and then clear your site cache and then check back.
In case if the issue is still there then provide me your login credentials so I will check myself and help you out.
Best Regards.