I can't guarantee this will work, but if it's an invoice issue as it seems to be, and the following suggestion is workable for you, it stands a pretty decent chance of avoiding the multiple payments received when one was sent.

You can set up automatic postage discounts, thus easily eliminating the need for buyers to wait for a combined postage invoice. You can choose from several different options when it comes to applying discounts, for example each additional purchase is X amount after the first P&H cost, or even free.

Another is to subtract from additional postage costs (eg $1 of the P&H quote for each additional item - it can get a bit confusing for buyers trying to work out what the total might be, though). There's also a percentage discount option, and a postage cap option (eg pay no more than $5 P&H).

You're able to set up various postage rules under different profile names, then you can edit your listings in bulk via Selling Manager and add them to the listings that you want them to apply to. (Note: if you create a flat postage rule and a promotional postage rule, the promotional rule will always override the flat rule if they are applied to the same listings - that way, you can have it do something like this; Flat Rule - 50c per additional item, Promotional Rule: $5 postage cap, so if someone buys 5, they'll pay the $2.50 extra, but if someone buys 20, the most P&H they'll pay is $5). 

Make sure that, in your site preferences, you have it set up to allow combined purchases (you can set it to a variety of time frames, mine is currently set up so that purchases will combine automatically over a period of 7 days. You can include items purchased outside of that time frame, eg a buyer buys 1 item, then 8 days later another, they won't automatically combine but you can include them in a manual invoice). 

I hope all that makes sense. If you need anything clarified, or help on how to get everything set up if you want to try it, just let me know.