The vast majority of timber gazebos, or certainly those sold on a commercial basis, tend to be pressure impregnated softwood and will or should come with a 10+ year guarantee against failure of wood parts due to rot/insect attack.
Whilst improvements to the treatment process have been made, such as incising the timber for better penetration, the actual preservative solution is perhaps not as aggressive as it once was. Hence the process is more controlled and end use specifications are used.
If you look around after a heavy storm, there will invariably be fences in a more horizontal position, and on close inspection, more often than not, these have decayed at ground level.
The most common cause for external decay in timber is fungal. For fungal decay to occur there will ideally be a mix of food (wood), air, water and the correct temperature, all which forms at ground level. Below ground this occurs more slowly due to lack of oxygen. You may see old timber barns or structures that have turned very grey and split from the action of wind and UV light though not rotten.
Of course, there are sites such as the coast and hills that are very windy, and the shelter needs to be built to stop it blowing over. Yes, concreting in is one option, though if this is the case then a higher specification of timber treatment must be used and even then it may still only come with a limited guarantee.
If possible, the best way to avoid this issue is not to create the situation in the first instance which is why we at Cabinco never concrete our posts in to the ground. Where it is known to be an issue, such as coastal Scotland, we bolt down the posts to cast concrete pads* raised off the pad by 18mm rubber damp proof course.
After installing these across the length and breadth of the UK over the past 17 years we are pleased to say that, to date, we have not had one blow away!