The value of rupee against dollar depends on the demand of $ vis-à-vis rupee. Also we need to remember that the exchange rate depends on a lot of other economic and political factors. It also depends on the expectations of how the exchange rate might move in the future.
2012-13 was a tough time for India on many fronts. The US economy was on a recovery and hence India saw a large amount of investment outflows. This was not an isolated pattern. Something similar was seen in many other emerging markets such as South Africa and Indonesia. This led to an increased demand for dollar and hence a depreciation in rupee.
Moreover, during this time, the expectations for the future of economy and the rupee were pretty bleak due to policy paralysis in the government. There were also a number of negative indicators working against the rupee such as the fiscal deficit and the falling industrial production numbers. Also during the first few months of 2012 (calendar year) crude was at its peak (around $106 per barrel) which put an additional burden on the rupee given India’s large crude imports.
Although the Fed was still buying large amounts of govt. bonds at this time one needs to remember that there were already talks of tapering going on. This helped shape the expectations of the investors who believed that Fed’s talks of tapering indicate a recovering and strengthening US economy. This further bolstered the dollar.
These were the prime reasons behind the decline of rupee during most of 2012 and 2013. Hope this explanation was helpful.