### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate

### What happened?

A provider budget entry with a duration but no numeric maximum removes that provider's deployments from the healthy set on current `litellm_internal_staging` at commit `65ca095d4d15a82372e53a547a2390a69f7e1797`

Inside [`_filter_out_deployments_above_budget`](https://github.com/BerriAI/litellm/blob/65ca095d4d15a82372e53a547a2390a69f7e1797/litellm/router_strategy/budget_limiter.py#L191-L235), this block runs inside the outer loop over deployments:

```python if provider in provider_configs: config = provider_configs[provider] if config.max_budget is None: continue ```

That `continue` advances the deployment loop. It does not only skip the provider comparison

The deployment is never appended to the returned healthy list and never reaches its deployment-budget or tag-budget checks

`BudgetConfig` allows `max_budget` and `budget_duration` to be independently optional, including the public aliases `budget_limit` and `time_period`, so a duration-only entry reaches this state

A missing maximum should mean that there is no numeric pro…