I'm not sure it's due to National decline at least not entirely. Personally I'd suggest it's got to do with defence spending (where a replacement would be funded from) not being a priority of this and every government since the War. The biggest priorities are Social Protection (£220bn), Health (£137bn) and Education (£97bn) whilst defence clocks in at £40bn. Therefore, if you're the Chief of the Defence Staff, looking at how much money you have do you spend it on replacing an aircraft that's old but works or on an equipment upgrade for the Royal Navy's Type 23 Frigates, or on integrating Brimstone onto the Tornado, or upgrading the L85 rifle to the A2 standard?
If defence had been a bigger priority for government then it might have been possible to afford to replace the Sea Kings which currently perform SAR. However, the job of the military is to defend the nation and deliver foreign policy objectives so SAR takes a back seat when it comes to getting a slice of an always dwindling budget.
Figures from page six of the 2013 Budget found here.