Simple answer is YES.

Like most sporting events there are rules and conditions.

There is a  very simple re-entry, because as yet you have not left the rally, if you have a flat tyre or an engine issue, you will likely stop in the rally stage or on the liaison route. You will change the tyre or fix the fault then carry onto the next Time  Control. 
In simple terms you have re entered. You might even do this is you come off the stage but drive back on. I have even seen crews roll, get on all 4 wheels and carry on..The Golden Rule is, you are not out unless you are officially told. 
PS If you roll or have a crash in stage and finish the stage, you must seek, at the first opportunity,  the Scrutineer’s permission to continue to the next time control.

Now to the more likely Re-Entry procedure.

Let’s assume you had a few issues in stage, you manage to struggle out but you have run out of time to get to the next control or you need to make a better repair before driving fast again.

Firstly speak to the Competitor Liaison Officer and let them know you wish to re-enter the rally at the next re-entry point. In the Iceland Hill Rally these re-entry times are at the beginning of each Leg, typically the day has 2 Legs, morning and afternoon.

Then repair the car and seek the chief scrutineer and ask him to verify that your car is fit to rally.

The Clerk of The Course along with other staff, will allocate you a new start time. This start time will place you in a similar position to your last start position based on stage times that you completed.

This might be adjusted if it is felt your vehicle is no longer going to be as quick, that would come from your information and that of the scrutineer.

You can miss more than one Leg, but to be classed as a finisher you must complete 50% of the stage miles and drive through the final control without assistance.