Stock Management software integrating with Magento

My client, business selling  goods B2B and B2C currently uses Xero/DEAR/ and Magento integrations to manage books, inventory and website sales. Payments from website sales are collected via REALEX application.

 The process, which I'd assume is common to numerous businesses described below:

1. An order is placed on the website (Magento)
2. Payment is collected via Realex application (on DEAR)
3. The order is transferred to DEAR inventory
4. Once sale is completed sales and inventory transactions gets transferred to Xero

 The expectation of the  process is that once an order is   activated on the website, it would seamlessly gets transferred to DEAR software, payment received for the order will get seamlessly transferred to Xero and applied to the  sales invoice generated by this order. 

However, it is not a case:

1. Random orders are not getting transferred from the Website to DEAR
2. Only Random payments collected via REALEX application are getting transferred to Xero, and 
3.  Only random payments are getting applied to sales invoices on Xero

To aid  the above lots of manual interventions is required, which of course impedes my clients plans to expand websales, for at the moment, with the problems above it would be unsustainable.All of the above only applies to web sales and solution is sought for it only.

 The biggest problem is that  DEAR inventory support is very unhelpful, refusing to collaborate with website managing  groups, and  of course a lot is bounced off as fault of third parties, because of multiple integrations. 

   Hope the community will offer me some advice,  on possible applications, or solutions.