It seems (clearly!) to be a bug in the preprocessing for the new convex optimizer. Use one of the other methods (e.g. `"DifferentialEvolution"`

):

```
Trace(
NMaximize(E^(-x^2) - 1, x),
_Optimization`MinimizationProblem,
TraceForward -> True,
TraceInternal -> True
)
```

Workaround:

```
NMaximize(E^(-x^2) - 1, x, Method -> "DifferentialEvolution")
(* {0., {x -> -5.45643*10^-9}} *)
```

Alternatively, you can turn off the convex minimizer:

```
Block({Optimization`UseConvexMinimize = False},
NMinimize(-(E^(-x^2) - 1), x)
)
(* {0., {x -> -5.45643*10^-9}} *)
```