There are no restriction to how many times user can stake on beacon with EigenPodManager on EigenPod, thus all of them will have the same _podWithdrawalCredentials() and I think first deposit will be lost.
src/contracts/pods/EigenPod.sol#L159
There are some ways users can make a mistake by calling it twice or they would like to create another one.
Ive looked into rocketpool contracts; they are not allowing users to stake twice with the same pubkeys, so I think its important to implement the same security issue.
contracts/contract/minipool/RocketMinipoolDelegate.sol#L235
Same safe thing done in frax finance: 
src/frxETHMinter.sol#L156
POC
You can look at rocketpool contracts and borrow their logic:
ChaoticWalrus (EigenLayer) disagreed with severity and commented:
Alex the Entreprenerd (judge) decreased severity to QA and commented:
Alex the Entreprenerd (judge) commented:
For this audit, 13 reports were submitted by wardens detailing gas optimizations. The report highlighted below by neutiyoo received the top score from the judge.
The following wardens also submitted reports: 0xSmartContract,
turvy_fuzz,
pontifex,
niser93,
0xnev,
QiuhaoLi,
Aymen0909,
ihtishamsudo,
tonisives,
clayj,
ReyAdmirado and
naman1778.
