The reason is that it cost too much to put a series on hiatus.

When a (live action) production goes on stand-by/hiatus, you always lose key players and key elements. It's far more than the cast, it's all the show's key creative team down to the producers you risk will have moved on when you're ready to start again. Show creators, writers, filmmakers, key production people, key designers, VFX teams, service houses, score composer etc. - they won't twiddle their thumbs for a year or two to stay available fro you when you're ready to start again. Everyone's replaceable, but there's a cost associated to that. Same for the actors. Just for the VFX I know more intimately, there's no garantee the material, data banks of established recipes/elements, and all the softwares you use and paid to get developped for a series (the softwares are mostly off the shelf for TV, the extra programming like scripts, plug-ins, recipes for effects often aren't) will still be usuable two or three years from now. If a series is under contract and ongoing, a post house will manage things so this doesn't happen (ie: some key equipment won't be discarded or upgraded until you don't them need anymore or there will be a smooth gradual transition to the new systems etc.), but if there's a hiatus in production they won't. Whenever a project ends, several changes (both in staff and equipment) are made to meet the requirements for the new contracts. If you start again later, it will cost you much more than merely continuing would have. The development of some VFX (e.g. 3D wolves) is far more costly than their later use to create specific shots.

For a few months of hiatus you make deals with the providers and people (that's what they do to keep key staff and cast members onboard between seasons, basically a contract for the next one, with costly cancellation clauses and often some advances), but for a long hiatus or one of unknown duration that's not a possible avenue.

They would have to put back a team together later and would have to replace several key players, and no doubt would have to recast a few parts too. Putting the show back in production a year or two (or three.. it's Martin after all) later would be a long process (it took three years to put it in production. Putting it back in production after a hiatus would be faster, but nowhere as fast as putting a season in production - somewhere in-between, around a year or 18 months probably - and very costly, not quite equal but similar to what it took and cost to develop the show and put it in production for the first season. It's one of the real reasons why campaigns to bring back on the air cancelled shows virtually never work. The window of opportunity for another network to make a deal with the producers after a cancellation elsewhere is quite short.

Other sources of problems would be storage of sets, props, costumes (expensive enough that in big movie franchises they often decide to scrap everything and make them again for the next movie, TV rather tends to live with the storage costs for the few months of hiatus between seasons, which they do by paying part(if sets are stored) or the totality (if sets stay mounted) of the lease on studios for the months they're not using them) and deals made to use locations, studios etc.

It would also complicate a lot HBO's programming to have a series on hiatus they wouldn't know exactly when they'll get again. And putting a show on hiatus would be a gamble regarding its ratings.

All in all, this isn't a realistic option for HBO, and we already know Martin has provided the show creators with material in case they catch up to his publishing schedule at some point.

What sounds plausible, in the right circumstances, is that the production of the show goes on (with increased participation from Martin in the writing, no doubt) but HBO agrees to delay the broadcast for a season, or a few months, to leave Martin time to publish the last volume. By right circumstances, I mean he's close to finishing it and a publication date or deadline is set, to which he/Bantam would have to abide and otherwise HBO could broadcast the show if they don't meet it. That's not ideal for HBO, but neither would having the conclusion of a book series that took forever to write (it will likely reach the two decades mark before it's done) being scooped/spoiled by its TV adaptation be any good for Bantam and GRRM (might not be positive for HBO either, if the portion of Martin's readers who decide to wait for the book first and watch the series on BR after is sizeable). I suspect all sort of provisions and plans are part of the contracts already, but none of that will of course be made public (the most they were willing to say was that there was provisions in place so the series wouldn't have to stop, which was a way to nick in the bud any "don't watch, that series will be forced to stop in the middle because Martin won't finish it in time" internet campaign)

There is a fair chance he does, if the writing goes as it did for ACOK/ASOS rather than the way it did for AFFC/ADWD - but Martin's confidence as to when he'll finish an ASOIAF novel isn't worth much anymore, not until he's reaching the end of one anyway!

In interviews (like the one for EW) he was fairly confident he'd finish first, saying the real danger was if they decided not to split ASOS in two seasons (they decided to split it, we know now), and if they then re combined AFFC/ADWD, with parts of book 6 (resolving some of the cliffhangers). In that case, he expected they could catch him in the middle of writing the final volume (which could trigger my "right circumstances" scenario), but otherwise he'd finish first. There is a fair chance he does (before broadcast at least, the last or two last seasons could go in writing and even production before the book is released), if the writing goes as it did for ACOK/ASOS rather than the way it did for AFFC/ADWD - but Martin's confidence as to when he'll finish an ASOIAF novel isn't worth much anymore, not until he's reaching the end of one anyway!