The problem here is pi.Steps[0] is null is Your Rejection Process going back a step? 

Have spent a few hours rewriting the code trying to make this work.

Currently I see major issue with this solution: if your Approval Step Rejection does not go to Final Rejection Step. ( i.e. you go back a step )

-- The processInstanceStep for that rejection is not inserted within the context of the current trigger.  So you can determine if a comment had been entered and hence you always fail validation when trying to reject an approval. 

Here is my updated method if you want to try this.

	public static void validateApproval(map<Id, Invoice__c> newInvoices,  map<Id, Invoice__c> oldInvoices)
	{
		map<Id, Invoice__c> rejectedInvoices = new map<Id, Invoice__c>();
		set<Id> rejectedInvoicesWithCommentsIds = new set<Id>();

		// Build a list of rejected approval processes
		for ( Invoice__c inv : newInvoices.values() )
		{
			Invoice__c oldInvoice = oldInvoices.get( inv.Id );

			system.debug('oldInvoice.Approval_Process_Status__c: ' + oldInvoice.Approval_Process_Status__c);
			system.debug('inv.Approval_Process_Status__c: ' + inv.Approval_Process_Status__c);

			if (( oldInvoice.Approval_Process_Status__c == 'Pending' || oldInvoice.Approval_Process_Status__c == 'Approved' )
				&& (inv.Approval_Process_Status__c == 'Rejected'))
			{
				rejectedInvoices.put(inv.Id, inv);
			}
		}

		if (!rejectedInvoices.isEmpty())
		{
			map<Id, ProcessInstance> latestInstance = new map<Id, ProcessInstance>();

			for (ProcessInstance pi : [	SELECT TargetObjectId, Status, CreatedDate,
	            	                 		(
	                                 		SELECT Id, ProcessInstanceId, StepStatus, Comments, CreatedDate
	                                 		FROM Steps
	                                 		WHERE StepStatus = 'Rejected'
	                                 		ORDER BY CreatedDate DESC
	                              			)
                               			FROM ProcessInstance
                               			WHERE TargetObjectId In
                                 		:rejectedInvoices.keySet()
                               			ORDER BY CreatedDate DESC
                              		])
    		{
    			system.debug('processInstance: ' + pi);
    			system.debug('steps.size: ' + pi.Steps.Size());

    			for ( ProcessInstanceStep pis : pi.Steps)
				{
					system.debug('pis: ' + pis);
				}

    			if (!latestInstance.containsKey(pi.TargetObjectId))
    			{
    				latestInstance.put(pi.TargetObjectId, pi);
    			}
    			else
    			{
    				ProcessInstance maxInstance = latestInstance.get(pi.TargetObjectId);
    				if ( maxInstance.CreatedDate < pi.CreatedDate  )
    				{
    					latestInstance.put(pi.TargetObjectId, pi);
    				}
    			}
    		}

			system.debug('latestInstance.values(): ' + latestInstance.values());


    		// only process the latest processInstance for any invoice
    		for ( ProcessInstance pi : latestInstance.values())
    		{
    			system.debug('pi: ' + pi);

    				ProcessInstanceStep latestPis = new ProcessInstanceStep();

					// only process the latest step of any processInstance
					for ( ProcessInstanceStep pis : pi.Steps)
					{
						system.debug( 'pis: ' + pis);
						system.debug( 'latestPis: ' + latestPis);
						system.debug( 'latestPis.comments: ' + latestPis.Comments);

						if ( latestPis.Id == null)
						{
							latestPis = pis;
						}
						else
						{
							if ( latestPis.CreatedDate < pis.CreatedDate)
							{
								latestPis = pis;
							}
						}
					}

					system.debug( 'Final latestPis: ' + latestPis );
					system.debug( 'Final latestPis.comments: ' + latestPis.Comments);

		      		if ( (latestPis.Comments == null) || (latestPis.Comments.trim().length() == 0) )
		      		{
		      			rejectedInvoices.get(pi.TargetObjectId).addError(
		          		'Operation Cancelled: Please provide a rejection reason! Select back button and enter a reject comment.');
		      		}
		      		else
		      		{
		      			Invoice__c completedInvoice = rejectedInvoices.get(pi.TargetObjectId);
		      			system.debug('reseting Approval_Process_Status__c for Invoice__c.Id: ' + completedInvoice.Id);
		      			completedInvoice.Approval_Process_Status__c = 'Pending';
		      		}

			}

		}

	}