When booking hotel rooms the cheapest option is normally advance payment, which you cannot canceled or changed, if booked with a credit card does the credit card company cover any loss if flights are delayed or cancelled or for some "real" reason you don't turn up?
Not generally, no. The hotel is offering you a cheaper rate in exchange for a non-cancellable advance payment. If you don't turn up, you've agreed to pay as part of the conditions for your booking, and the hotel will submit evidence of that if you try to submit a payment dispute for the charges.
Travel insurance may cover some or all of the cost, but note that travel insurance policies have very specific fine print on what exactly is covered. Some credit cards do include certain travel insurance benefits for trips purchased with the card. You'd need to check the details on that policy to see what limits and conditions apply and the process to make a claim. You can also buy separate travel insurance, either on a per-trip or annual basis.
You can also try to talk to the hotel (or the third-party booking site if you've used one; some third-party sites are well-known for trying to pressure hotels to waive cancellation charges) and see if they're willing to make an exception to the non-refundable policy. Whether they'll do so depends on the hotel's policy, and they have no obligation to do so beyond as a customer service gesture, but they may be willing to give you a refund entirely, shift your travel dates for you, allow you to rebook at another hotel within the same chain, or perhaps turn your payment into a credit you can use in the future. Call the hotel as soon as you know you won't be able to make it, and they're often willing to refund a missed night due to travel delays.
You will only be covered for such reasons, if your credit card also includes travel insurances, and it is a covered reason why you can't travel (e.g. if you get sick and you have a cancellation insurance included, which covers sickness). Most included insurances only cover "real" reasons, like sickness, sudden job loss (if not self inflicted).
A credit card without any insurance will not be helpful, if you need to cancel your trip for whatever reason. Only if the hotel cancels from their side and doesn't refund you your money, you can claim it back through the credit card company.