Are you 100% sure the action is configured in the client event for the “second” action? Check in Management Console > Workflow Server > Processes > Open the process and beneath roles you will see the actions. Check if the action is there for the “second” action.

Yes I am sure. in fact i created brand new actions with Infopath client events just to make sure. However I noted that once   I set up the Task Action Field of Activity A with Infopath Field A and then I do the same with Activity B and Infopath Field B. But when I go back to check   Activity A,  the Task Field  is linked with the Infopath Field for Activity B. I cannot manage to set them each with the corresponding Infopath field. Is this a bug?

Also I was looking on the K2 Management Console for the Processes node and is not there. I just have Administration, Managemnt and License Management and Process is not under them. Thank you! 

Not aware of any bugs regarding this, you can log a ticket with K2 support for further investigation.

I got confused only realised you are using BalckPoint now, you will not find the actions as I described, that is for BalckPearl. Sorry for that.

In BlackPoint do the following to see if the user has action rights:

Goto the portal > K2 Management > Settings > add the process there.  Once the process is added, in the navigation pane on the left > click Action Rights. You should not be able to view the different actions and add users (Manage Users) to give rights to action here.

Vernon