1) Check your contract
Try to find what it says about:
- Contract Renewal/Termination Notice (if they need to give notice before firing you or not renewing your contract)
- Employer's Termination Rights (if they can fire you for not having a proper visa)
- Any Obligations on Non-Renewal (see if they are obligated to pay for your plane fare home depending on how the contract ends, and if you have any additional obligations to the employer)
Make sure that you have prepared for the worst-case scenarios: not having your visa renewed, and having your contract expire/be terminated.
2) Check Austrian Visa Requirements
I am not familiar with Austrian visa requirements (and they differ by country, industry, etc. generally), but for many countries the visa is not actually tied to the employer. In other words, you need to have a sponsor to get the visa, but losing the job with the employer does not necessarily mean you lose the visa.
I would confirm the Austrian regulations and/or call the immigration service in Austria to find out what the status of your visa is if your current contract gets terminated for whatever reason. The best-case scenario is that you learn you have 8 months left on the visa to find similar work in Austria, and can start looking 6 weeks early. The worst-case scenario is that it is tied to your employment and you should plan to leave in 6 weeks if required.
Be sure to ask if there is a grace period after the employment ends to move out of the country. The last thing you want is the contract ending on a Friday, and having to leave the same day with all your stuff.
3) Talk to your Boss
Once you know what your legal requirements are in regards to employment and living/working in Austria, it's time to talk to your boss.
Be positive! Explain the good things -- that you like working there, you want to keep working there, and that you enjoy the company and the country (assuming it's an Austrian company and an Austrian boss). Explain that your contract is ending in 6 weeks, and what you found out from 2) above about visa requirements and how challenging it will be if your contract doesn't get renewed.
I would make a simple request: if you guys want to renew my contract, could I please have a signed copy of the renewal in 2 weeks?
4) Prepare for the Worst
Unfortunately, because of stringent visa requirements for people from less developed countries to the EU/US/Japan especially, many employers will take full advantage of highly educated candidates by paying them less, working them harder, and then getting rid of them. I am not saying your employer is going to do that, but be prepared for the worst.
Whenever working in a foreign country, it is most important for you to understand better than your employer about what your rights are in regards to employment and residency in that country, so that they lose some of their ability to take advantage of you.
For instance, in Japan, many employers will tell their (foreign) employees that their work visa is tied to employment, and if they ever break the contract the employer can get them deported. This is not true, but it scares a lot of new people with no Japanese skill in to continuing with less-than-ideal working conditions because they feel they have no choice.
Do not let an employer take advantage of you, and make sure you understand your situation well enough to feel comfortable even in the worst-case scenario. Moving to another country is stressful enough without having to worry about visa requirements.