Lots of time & cost has incurred in project initiation. close the project & book the expenses as sunk money. or pump in more funds & continue.

there us no certain role for this , some time only sense of humor can decide the continuois of projects.

In my opinion:

Lost of Cost and Time it will effect your Scope.

so, you have to close the Project.

study the project risk more and more And then select the path

Project Initiation phase broadly consists of :

1) Committment of the sponsor to own and fund the project.

2) Appointment of Project Manager and award of Project Charter to the PM.

3) High Level Planning with respect to Scope, Deliverables,Time, Cost, Risk, Stakeholders.

This stage requires least amount of time and negligible costs. 

The question states that - Lots of time & money has been spent in the project initiation. 

This senario indicates that the Project Sponsor whose involvement is of very high importance in the initial stages of the project is not committed and/or competent to complete the project successfully but is taking up the project out of compulsion.

The best option is thus to close the project immediately instead of pumping in more money as nothing tangible has been achieved or is likely to be achived in near future.

اعتقد انه يجب ضخ المزيد من الأموال والإستمرار ومحاولة تجنب الأخطاء والإخفاقات.

You have to asse first how much money spent and if it is recovarable. Then you have to study the possibility of creating a crushed program to return back to schedule .

If the crushed program is possible , revise yourbudget, if the crushed program will lead to more impact then you decision should be to shut down the project. If on the contrary, the analysis shows minor impact you have to go on seeking break-even and the company reputation in the market.