Interest rate parity: Counter intuitive What is the basis for interest rate parity to hold?
I know, the reason stated is excess returns

Excess returns as such should not be the reason for a currency depreciation. for e.g. when we posit that forward rate converge to the spot rates over time and back by arbitrage argument it is actually because forward prices, if less than spot prices, would result in an increase in the demand for forwards and subsequently increase its price. (talking about long positions here). 

Hence, in relation to interest rate parity, excess returns(which is wrongly stated sometimees as arbitrage) should put downward pressure on the interest rates. (you keep investing more and more money in a bank at a given rate obviously it cant keep it up and has to lower the rates, also it now has a lot of reserves so it wants to lend again leading to lowered rates) why it should affect the exchange rate beats me.

To the contrary a high interest rate(say of country A) should put upward pressure on exchange rates(foreign/home); People want to invest more into A's banks so they convert more foreign currency to A and hence the A's currency should appreciate
In your last paragraph you write "high interest rate in Country A". There is no such thing. There is higher interest rate, per some given criterion. Say higher than historical average. In out case, it is "higher interest rate in Country A compared to the interest rate in Country B".  

So your last paragraph says that if returns (from nominal interest rates) in Country A are higher than returns (from nominal interest rates) in Country B, that would put upward pressure to the exchange rate (units of currency B per one unit of currency A): people will demand more currency A, etc. 

Now a different but equivalent  way to say "higher returns in A than in B" is "excess returns", in the specific context we are talking about. Of course the term "excess returns" is very general and can be used in any situation. Sometimes it may used to mean "abnormal" returns (in some sense and again compared to some base). But in the specific situation we are talking, it has the exact same meaning with "higher returns from nominal interest rates in Country A compared to returns (from nominal interest rates) in Country B". 

So moving to your penultimate paragraph you say that "if returns in A are higher than returns in B, that should put downward pressure on the interest rates in country A (because funds flow in), and it should leave the exchange rate unaffected".

Although there is logic to the mid-term effect of an increase in the flow-in of funds, still it appears that your last paragraph already answers the question "why should exchange rate be affected?", stated  in your penultimate paragraph.

ADDEDNUM
Responding to the OP's comment, let's write the Uncovered Interest Rate Parity expression

$$(1+i_{A,t}) = \frac {S^e_{A|B, t+1}}{S_{A|B, t}} (1+i_{B,t})$$
where $S_{A|B}=$ units of currency A per unit of currency B.
This is the claim.  The numerator is the expected future exchange rate

Assume that $i_{A,t} &gt; i_{B,t}$. Standard economic logic (and a few assumptions on ability to invest over borders), says that then investors would want to invest in country A. To do that they will increase demand for currency A. This should lead to appreciation of currency A. Does the UIRP say something like that?  

If $$i_{A,t} &gt; i_{B,t} \implies 1+i_{A,t} &gt; 1+i_{B,t}$$
and so the UIRP asserts that we must have

$$\frac {S^e_{A|B, t+1}}{S_{A|B, t}} &gt; 1 \implies S^e_{A|B, t+1} &gt; S_{A|B, t}$$

Given how $S$ was defined the last inequality means that we expect that the currency will depreciate. Indeed, in the future. Because, what is affected in the first place by the reaction of the investors is $S_{A|B, t}$, not $S^e_{A|B, t+1}$. The reaction of the investors will decrease $S_{A|B, t}$ (which reflects the appreciation of currency A), creating expectations of future depreciation, i.e. leading to $S^e_{A|B, t+1} &gt; S_{A|B, t}$, as the UIRP asserts. Why should we expect depreciation of currency A in the future, compared to the present? Because the inflow of funds in country A will eventually pressure $i_{A,t}$ downwards, as the OP remarked, investors will stop loving currency A so much, demand for it will fall, hence depreciation.  

The UIRP therefore compacts two effects from a discrepancy in interest rates: a first effect of currency appreciation and a second (expected) effect of currency depreciation in the future.