SQL Server Dynamic Resetting Running Balance

Realised that the data in your question is essentially the source data and have been able to come up with the below. It isn't exactly pretty but it provides the correct output. Explanations on how it works are in the comments:

declare @t table(Tran_DateSK int, Amount decimal(10,2), Running_AccountFees int, Overlimit_Balance decimal(10,2), Restart_Calc bit, Actual_Calc decimal(10,2));
insert into @t values(20200217,39,39,3867.76,0,39),(20200217,50,89,3867.76,0,89),(20200316,39,128,4735.52,0,128),(20200316,50,178,4735.52,0,178),(20200324,50,228,2685.52,0,228),(20200330,50,278,49.52,1,49.52),(20200415,39,317,49.52,1,49.52),(20200515,39,356,3917.28,0,88.52),(20200515,50,406,3917.28,0,138.52),(20200519,50,456,3467.28,0,188.52),(20200604,50,506,3017.28,0,238.52),(20200609,50,556,2167.28,0,288.52),(20200611,50,606,49.28,1,49.28),(20200615,39,645,3917.04,0,88.28),(20200615,50,695,3917.04,0,138.28),(20200616,50,745,3017.04,0,188.28),(20200616,50,795,3017.04,0,238.28),(20200619,50,845,2567.04,0,288.28),(20200624,50,895,47.04,1,47.04),(20200715,39,934,47.04,1,47.04);

with t as
(
    select Tran_DateSK
          ,Amount
          -- Check if the Running_AccountFees are over the Overlimit_Balance
          ,case when sum(Amount) over (order by Tran_DateSK,Amount,Overlimit_Balance rows unbounded preceding) > Overlimit_Balance
                        -- If so, check if the Running_AccountFees in the previous row were also over the Overlimit_Balance
                  then case when (sum(Amount) over (order by Tran_DateSK,Amount,Overlimit_Balance rows unbounded preceding) - Amount) > lag(Overlimit_Balance,1,0) over (order by Tran_DateSK,Amount,Overlimit_Balance)
                            then 0      -- and in those instances this means multiple Restart_Calcs in a row, so set the Amount to zero as we don't want to increase the fees when calculating the Actual_Calc
                            else Amount
                            end
              else Amount
              end as Amount_Adj

          ,sum(Amount) over (order by Tran_DateSK,Amount,Overlimit_Balance rows unbounded preceding) as Running_AccountFees
          
          ,lag(Overlimit_Balance,1,0) over (order by Tran_DateSK,Amount,Overlimit_Balance) as Prev_Overlimit_Balance
          
          ,Overlimit_Balance

          ,case when sum(Amount) over (order by Tran_DateSK,Amount,Overlimit_Balance rows unbounded preceding) > Overlimit_Balance
                then 1
                else 0
                end as Restart_Calc
    from @t
)
,b as
(
    select *
          ,case when Running_AccountFees > Overlimit_Balance    -- If this row is the first in a possible series of balance resets
                    and sum(Amount_Adj) over (order by Tran_DateSK,Amount,Overlimit_Balance rows between unbounded preceding and 1 preceding) <= Prev_Overlimit_Balance
                then Overlimit_Balance      -- Take the Overlimit_Balance and subtract the *Adjusted* Running_AccountFees
                     - sum(Amount_Adj) over (order by Tran_DateSK,Amount,Overlimit_Balance rows  between unbounded preceding and 1 preceding)
                     - Amount_Adj
                else 0
                end as Reset_Bal
    from t
)
select Tran_DateSK
      ,Amount
      ,Running_AccountFees
      ,Overlimit_Balance
      ,Restart_Calc
      -- For each *Adjusted* Running_AccountFees, apply the most negative Reset_Bal value, as this will contain the entire amount that needs to be reset from the current *Adjusted* Running_AccountFees to get the correct Balance_Calc
      ,sum(Amount_Adj) over (order by Tran_DateSK,Amount,Overlimit_Balance rows unbounded preceding)
        + min(Reset_Bal) over (order by Tran_DateSK,Amount,Overlimit_Balance rows unbounded preceding)
        as Balance_Calc
from b
order by Tran_DateSK;

Output

+-------------+--------+---------------------+-------------------+--------------+--------------+
| Tran_DateSK | Amount | Running_AccountFees | Overlimit_Balance | Restart_Calc | Balance_Calc |
+-------------+--------+---------------------+-------------------+--------------+--------------+
|    20200217 |  39.00 |               39.00 |           3867.76 |            0 |        39.00 |
|    20200217 |  50.00 |               89.00 |           3867.76 |            0 |        89.00 |
|    20200316 |  39.00 |              128.00 |           4735.52 |            0 |       128.00 |
|    20200316 |  50.00 |              178.00 |           4735.52 |            0 |       178.00 |
|    20200324 |  50.00 |              228.00 |           2685.52 |            0 |       228.00 |
|    20200330 |  50.00 |              278.00 |             49.52 |            1 |        49.52 |
|    20200415 |  39.00 |              317.00 |             49.52 |            1 |        49.52 |
|    20200515 |  39.00 |              356.00 |           3917.28 |            0 |        88.52 |
|    20200515 |  50.00 |              406.00 |           3917.28 |            0 |       138.52 |
|    20200519 |  50.00 |              456.00 |           3467.28 |            0 |       188.52 |
|    20200604 |  50.00 |              506.00 |           3017.28 |            0 |       238.52 |
|    20200609 |  50.00 |              556.00 |           2167.28 |            0 |       288.52 |
|    20200611 |  50.00 |              606.00 |             49.28 |            1 |        49.28 |
|    20200615 |  39.00 |              645.00 |           3917.04 |            0 |        88.28 |
|    20200615 |  50.00 |              695.00 |           3917.04 |            0 |       138.28 |
|    20200616 |  50.00 |              745.00 |           3017.04 |            0 |       188.28 |
|    20200616 |  50.00 |              795.00 |           3017.04 |            0 |       238.28 |
|    20200619 |  50.00 |              845.00 |           2567.04 |            0 |       288.28 |
|    20200624 |  50.00 |              895.00 |             47.04 |            1 |        47.04 |
|    20200715 |  39.00 |              934.00 |             47.04 |            1 |        47.04 |
+-------------+--------+---------------------+-------------------+--------------+--------------+