If an Emblem of yours is deleted, Then it was obviously reported and was found to be in violation of the EA Terms Of Service.
Any content you upload ( or create using the tools built into battlelog ) Is subject to removal if it violates the EA Terms Of Service.
The best way to avoid action like that, Is to ensure your UGC ( User Generated Content ) does not violate TOS.
https://tos.ea.com/legalapp/WEBTERMS/US/en/PC/#section5
You are responsible for your UGC. You may not upload UGC that infringes a third party’s intellectual property rights or that violates the law, this Agreement or a third party’s right of privacy or right of publicity.
EA may, in its sole discretion, remove, edit or disable UGC for any reason, including if EA reasonably determines that UGC violates this Agreement. EA does not assume any responsibility or liability for UGC, for removing it, or not removing it or other Content. EA does not pre-screen all UGC and does not endorse or approve any UGC available on EA Services.
When you contribute UGC, you grant to EA, its licensors and licensees a non-exclusive, perpetual, transferable, worldwide, sublicensable license to use, host, store, reproduce, modify, create derivative works, publicly perform, publicly display or otherwise transmit and communicate the UGC, or any portion of it, in any manner or form and in any medium or forum, whether now known or later devised, without notice, payment or attribution of any kind to you or any third party. You also grant to all other users who can access and use your UGC on an EA Service the right to use, copy, modify, display, perform, create derivative works from, and otherwise communicate and distribute your UGC on or through the relevant EA Service without further notice, attribution or compensation to you.–
So yeah, Use non-tos-violating UGC and you’re good.