Do we know if our universe is stable?

One of the most intriguing consequences of the Higgs boson discovery is that its mass places the Standard Model near the border between absolute stability and metastability, i.e. our universe is unstable, but should last for an astronomically long time. This conclusion is based on effective potential calculations which involve some suspicious elements: for example, the stability criteria apparently depends on gauge. Can we establish the fate of our universe using only self-consistent methods?